Find sin(a)& cos(b), tan(a)& cot(b), and sec(a)& csc(b).

Part A)

Part B)

Part C)

Step-by-step explanation:

Part A) Find

we know that

If two angles are complementary, then the value of sine of one angle is equal to the cosine of the other angle

In this problem

---> by complementary angles

so

Find the value of in the right triangle of the figure

---> opposite side divided by the hypotenuse

simplify

therefore

Part B) Find

we know that

If two angles are complementary, then the value of tangent of one angle is equal to the cotangent of the other angle

In this problem

---> by complementary angles

so

Find the value of the length side adjacent to the angle alpha

Applying the Pythagorean Theorem

Let

x ----> length side adjacent to angle alpha

simplify

Find the value of in the right triangle of the figure

---> opposite side divided by the adjacent side angle alpha

simplify

therefore

Part C) Find

we know that

If two angles are complementary, then the value of secant of one angle is equal to the cosecant of the other angle

In this problem

---> by complementary angles

so

Find the value of in the right triangle of the figure

Find the value of

---> adjacent side divided by the hypotenuse

simplify

therefore

answerthe vertex form

step-by-step explanation: