Question

tan(theta)=−3/4 and cos(theta)>0. Find sin(theta), cos(theta), cot(theta), csc(theta), and sec(theta).

Answer 1

find the hypotenuse by pythagoras or memory
then take the appropriate ratios, being mindful of what quadrant you are in so you can put the right sign \(+\) or \(-1\) in your answer

Answer 2

It says cos(theta)>0 So..it must be in 4th quadrant

Answer 3

That's what I don't understand. How do I know which quadrant I am in when cos theta is > 0?

Answer 4

OH. Okay. Let me try :)

Answer 5

forget about the signs until the answer
sides of a triangle are positive
you are in quadrant 4 because cosine in positive but sine is negative.

Answer 6

from the picture we see cosine is \(\frac{3}{5}\) and you know it is positive because you are told

Answer 7

oops i mean cosine is \(\frac{4}{5}\) sorry

Answer 8

sine is \(-\frac{3}{5}\) you get the \(\frac{3}{5}\) from the triangle, and it is negative because you are in quadrant 4 etc

Answer 9

OH i get it okay. one second. THANK YOU!

Answer 10

so sin = -3/5; cos = 4/5; cot 4/3; csc -4/5; sec 5/4?

Answer 11

cot = -4/3**

Answer 12

Yup....

Answer 13

your cosecant is wrong, all others are right

Answer 14

Sec and Cos are only +ve..

Answer 15

and the cotangent

Answer 16

oh you corrected it

Answer 17

cosec = 1/ sin x

Answer 18

cosec x = -5/3

Answer 19

I got: sin -3/5; cos 4/5; cot -4/3; csc -5/3; sec 5/4 correct?

Answer 20

thank you!