Question

Evaluate each trigonometric equation for θ.

Answer 1

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

Explanation:

Let us revise the trigonometry functions

• Sin(x) = opposite/hypotenuse

• Cos(x) = adjacent/hypoteouse

• Tan(x) = opposite/adjacent

• Csc(x) = hypotenuse/opposit

• Sec(x) = hypotenues/adjacent

• Cot(x) = adjacent/opposite

In the given figure

The opposite side to angle Ф = 8

The adjacent side to angle Ф = 15

Find the hypotenuse using Pythagoras' theorem

`Hypotenuse = \sqrt{8^(2)+15^(2) }`

`Hypotenuse = √(64+225)`

`Hypotenuse = √(289)`

`Hypotenuse = 17`

Let us use the rules above to find the trigonometry functions

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8