We are told that tanθ=1, and that 𝜃 is in Quadrant II. From this we know...

Question

csc ?

sin?

Cot?

is it one of these? and if so how?

Answer 1

We are going to need to recall some right triangle trig and reference angles to tackle this problem. Since tanθ =1, we can construct a right triangle in Q1, with the reference angle, say r, of θ. By SOH-CAH-TOA, this triangle with have both legs of length 1, and by the Pythagorean Theorem, hypotenuse, sqrt(2).

Now from this, we can find all the other trigonometric functions! Using SOH-CAH-TOA again on our triangle, we can find sin r = 1/sqrt(2), cos r = 1/sqrt(2). However, this is only for the reference angle r of θ. We need to transfer ourselves back to Q2. Recall that sin is positive and cosine is negative in Q2. Hence,

sinθ= 1/sqrt(2) = sqrt(2)/2 (if you choose to rationalize)

cosθ=-1/sqrt(2) = -sqrt(2)/2.

The remaining trig functions are found by remembering they are the reciprocals of sine, cosine, and tangent.