Question

Given right triangle ABC with right angle C and cos A= 1/3, which of the following expressions is also equal to 1/3?

a. sinB
b. sin(90°-A)
c. sin(90°-B)
d. Both A and B are correct​

Answer 1

Answer:D

Explanation:

So we know that:

To co-function identities state that:

Therefore, this is the same as:

B is correct.

Additionally, recall that in a right triangle, the two other angles must add up to 90. In other words:

Subtract A from both sides:

So we can make the substitution:

Thus, A is also correct.

The correct answer is D .

Answer 2

D

Explanation:

So we know that:

`\cos(A)=1/3`

To co-function identities state that:

`\cos(\theta)=\sin(90\textdegree-\theta)`

Therefore, this is the same as:

`\cos(A)=\sin(90\textdegree-A)`

B is correct.

Additionally, recall that in a right triangle, the two other angles must add up to 90. In other words:

`A+B=90`

Subtract A from both sides:

`B=90-A`

So we can make the substitution:

`\sin(90-A)=\sin(B)`

Thus, A is also correct.

The correct answer is D .