Trigonometry: Given sin theta= 2/3 use trig. identities to find the values of the following

Question

Given sin theta= 2/3 use trig. identities to find the values of the following

a. sin( (pi/2) - theta)

b. tan theta

c. cos theta

d. sec theta

e. csc theta

Show the trig identity used for each. Please and thank you!

Answer 1

Given sin theta= 2/3 use trig. identities to find the values of the following

a. sin( (pi/2) - theta)

b. tan theta

c. cos theta

d. sec theta

e. csc theta

Show the trig identity used for each. Please and thank you!

Hello,

It's hard without being able to write these symbols, or a picture, but I'll try.

So we'll need to find the values of the OPPosite side, ADJacent side, and HYPotenuse (SOH CAH TOA).

We know from sin theta = 2/3 that the OPP is 2 and HYP is 3.

Using Pythagorean theorem we can find ADJ. a² + b² = c². Plus in 2 for a and 3 for c. We get squareroot(5) for b.

So OPP = 2

ADJ = squareroot(5)

HYP = 3

Use these to plug them in for tan and cos. Using SOH CAH TOA.

For part d, secant, sec is 1/cos. So just flip the numbers.

For part e, csc is 1/sin.

I hope this helps!

-Margaret