nikakuz
Name five x values for which the sine function equals to 0. Please help!!
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Mertsj
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Are you familiar with the unit circle?
nikakuz
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no
Mertsj
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Then find the inverse sine of 0 and and 360 to that answer repeatedly until you have 5 values.
nikakuz
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how?
Mertsj
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With your calculator
nikakuz
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I don't know how though
Mertsj
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inverse sin 0 enter
Mertsj
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What in the world are you doing that you don't know anything about the unit circle and don't know how to use your calculator?
nikakuz
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i put sin 0 enter and the answer was 0 how do i get 5 values?
nikakuz
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trying to learn from an oonline classs
Mertsj
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|dw:1375670932781:dw|
Mertsj
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Have you ever seen that before?
nikakuz
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yeah
Mertsj
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That is the unit circle. It is called the unit circle because the radius is 1 unit. The sin is like y.
Mertsj
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Do you see that the y value is 0 at 0 degrees and 180 degrees?
nikakuz
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yes
Mertsj
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Your problem says to give 5 values for which the sin is 0. There are two of them right there: 0 degrees and 180 degrees. If we would go around the circle another time, we would come to 360 degrees and 180+360 which is 540 degrees. Are you with me?
nikakuz
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sorta.. so it would be 0,180,540?
Mertsj
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0,180,360,540...
Just keep adding 180 degrees because every 180 degrees, the y value (which is the sin) is 0.
Mertsj
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Or, instead of rotating counterclockwise, we could go clockwise and then the angles would be -180, -360, -540, ...
nikakuz
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ohh ok thank you! i have the same question exept its cosine value
Mertsj
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Same thing except the cosine is like x.
Mertsj
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So where is the cosine 0 on the unit circle?
nikakuz
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um im not sure
Mertsj
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Look at the picture I drew. For what angles is the x value 0?
Mertsj
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|dw:1375671563924:dw|
Mertsj
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How many degrees is that?
nikakuz
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90?
Mertsj
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Yes.
Mertsj
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And what is the next angle where the x value is 0?
nikakuz
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so it would be 90 180...?
Mertsj
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|dw:1375671659091:dw|
nikakuz
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270?
Mertsj
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yes. so the x value is 0 at 90, 270, 450, 630...
nikakuz
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thank you soo much i just have one more
Mertsj
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Or at -90, -270, -450...
nikakuz
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same but tangent function
Mertsj
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Do you know the definition of tangent?
nikakuz
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umm no
Mertsj
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tangent is equal to sin over cos
Have you ever heard that?
nikakuz
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i think ive heard it
Mertsj
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\[\tan x=\frac{ \sin x}{\cos x}\]
Mertsj
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The only way a fraction can be 0 is for the numerator to be 0. So the tangent is 0 whenever the sin is 0
nikakuz
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ok so then wht
Mertsj
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Are you trying to answer this question: Give 5 angles who tangent is 0?
nikakuz
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the question is name five x values for which the tangent function equals to 0
Mertsj
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Could you answer this question: Name five x values for which the sine function equals to 0?
nikakuz
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yeah we already did that one
Mertsj
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So did you read this post which I made a few moments ago:
"The only way a fraction can be 0 is for the numerator to be 0. So the tangent is 0 whenever the sin is 0"
nikakuz
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yeah i read it but i don't understand
Mertsj
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The sin of 180 degrees is 0. Therefore the tangent of 180 degrees is also 0
The sin of 0 degrees is 0. Therefore the tangent of 0 degrees is also 0
The sin of 360 degrees is 0. Therefore the tangent of 360 degrees is also 0
The sin of 540 degrees is 0. Therefore the tangent of 540 degrees is also 0.
nikakuz
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so my answer would be exactly the same as the sine one?
Mertsj
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Let's make sure you understand this.
Mertsj
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What is the sin of 180 degrees?
nikakuz
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0
Mertsj
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What is the cosine of 180 degrees?
Mertsj
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\[\tan 180^{o}=\frac{\sin 180^{o}}{\cos 180^{o}}=\frac{0}{-1}=0\]
Mertsj
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I guess you've gone. Good luck.
nikakuz
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yeah i get it thank you soo much!!!!