Question

I really need help with thease

1. In the figure below, sin space alpha space equals space 2 over 3. Choose the TWO statements below that are true. 

cos space theta space equals space 2 over 3

cos space alpha space equals space 3 over 2

sin space theta space equals space 2 over 3

sin space beta space equals space 1 third

sin space beta space equals space 2 over 3

2. The degree of measure of an angle in a right tirangle is x and the sine x = 1 third. Which of these expressions are also equal to 1 third? Choose all that apply.


cos(x)


cos(x - 45 degree)


cos(45 degree - x)


cos(60 degree - x)


cos(90 degree - x)

Answer 1

see the attached figure with letters to better understand the problem

we know that
Part 1)
sin alpha=2/3
in the right triangle ABC
angle alpha+angle theta=90-------> by complementary angles
then
cos theta=sin alpha

in the right triangle EDC
angle beta+angle theta=90-------> by complementary angles
then
sin beta=cos theta

therefore
sin beta=sin alpha

the answer part a) is
cos space theta space equals space 2 over 3
sin space beta space equals space 2 over 3

Part 2)
we know that
if A and B are complementary angles
A+B=90°------> B=90-A
and
sin A=cos B
sin A= cos (90-A)

in this problem
sin x=1/3
then
cos (90-x)=1/3

the answer part b) is
cos(90 degree - x)