kittiwitti1 one year ago As θ increases from 0° to 90°, the value of cos θ tends toward which of the following? Answers available: 0 and 1. (Putting pos/neg infinity is wrong so I just need to decide which).

1. mathstudent55

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2. mathstudent55

The cosine of an angle is the x-coordinate of the point of intersection of the terminal side of the angle and the unit circle.

3. mathstudent55

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4. kittiwitti1

5. mathstudent55

When theta = 0 deg, cos(theta) = 1, since the x-coordinate of the point of intersection of the terminal side of of a zero-degree angle (in standard position) and the unit circle is 1.

6. kittiwitti1

I mean, the x-values are steadily decreasing so I assumed 0, but I am just making sure.

7. mathstudent55

Correct.

8. kittiwitti1

Thank you :)

9. mathstudent55

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10. mathstudent55

As theta goes from 0 deg to 90 deg, the x-coordinate goes from 1 to 0.

11. mathstudent55

You're welcome.

12. kittiwitti1

@mathstudent55 could you help me with this one as well? cos θ = 1/2 and θ terminates in QIV. So far I have this: http://prntscr.com/8dhn18

13. anonymous

$\sin(\theta)=\pm\sqrt{1-\frac{1}{4}}=\pm\sqrt{\frac{3}{4}}=\pm\frac{\sqrt{3}}{2}$ Since theta is in 4th quadrant, sin will be negative $\sin(\theta)=-\frac{\sqrt{3}}{4}$ There is a reason why you are given in which quadrant theta belongs to, so you can apply proper signs!

14. kittiwitti1

Thanks @Nishant_Garg :]

15. mathstudent55

@Nishant_Garg $$\large \sin(\theta)=\pm\sqrt{1-\frac{1}{4}}=\pm\sqrt{\frac{3}{4}}=\pm\frac{\sqrt{3}}{2}$$ $$\large \sin(\theta)=-\frac{\sqrt{3}}{\huge \color{red}{4}}$$ ?