Find the exact values of the six trigonometric ratios of the angle in the triangle 160 and 164

, , , , ,

Step-by-step explanation:

We notice that figure represents a right triangle, the hypotenuse has a length of 164 units and the leg opposite to has a length of 160 units. The sine of is:

The leg adjacent to is determine by the Pythagorean Theorem:

Then, the cosine of is:

Lastly, we determine the remaining trigonometric ratios by using these identities:

(1)

(2)

(3)

(4)

If we know that and , then the trigonometric ratios are, respectively:

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2