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If sectheta=5/3 and the terminal point determined by theta is in quadrant four then tantheta=4/3 costheta=3/5 sintheta=-2/5 csctheta=-5/4
which of these are true and how do you know?
wait so can we use the pythagorean theorum?
so 3^2+4^2=25 and that means the other side of the traingle is 5
3-4-5 is the most basic/common/recogniseable Pythagorean triple
alright and then that means that the answers are tantheta=4/3 and costheta=3/5 right?
but wait since its in quadrant four doesnt that mean that sin would be negative
yeah don't rush in you know this?? |dw:1443039749879:dw|
no i do not know that
so if its in the fourth quadrant does that mean that 4 and 5 are negtive?
the hypoteneuse is always +ve in the 4th, 4 is -ve, 3 is +ve the CAST thing allows you to predict the sign of the trig function without even looking that far, eg only tan is -ve in the 3rd of course that is because, in the 3rd, both opposite and adjacent are -ve [and hypoteneouse is always +ve, as mentioned] but the CAST shortcut allows you to "just know"
okay so just -3, 4, and 5 are the sides of the triangle that we use to determine the sin cos tan sec csc and cot?
i mean -4, 3, and 5
therefore costheta=3/5 and csctheta=-5/4