Question

Find the exact values of the remaining five trigonometric functions of 9.

Suppose is an angle in the standard position whose terminal side is in Quadrant IV and cot --2
√5
2N5
WB
5
b
d.
sin
sin
8-
Sin
COS
COS 8
sin 9-√√5.cos
√5
5
COS
8
-
csc --√√5. sec -
2√5
5 - CSC 9-√3. sec 0-
√3
2 CSC 8
2√5
5
√√3
sec
2
2√3
5
csc 9--√√3. sec –
tan
tan 8-
√5
tan
8"
tan
8H

Answer 1

sin(9°)=0.7454, cos(9°)=0.6667, sec(9°)=1.5000, csc(9°)=1.3416, tan(9°)=0.8944.

1. Quadrant Determination:

We are given that the angle 9° is in Quadrant IV. This means its cosine and secant are negative, while its sine, cosecant, and tangent are positive.

2. Using the Pythagorean Identity:

We can use the Pythagorean identity, sin^2(θ) + cos^2(θ) = 1, to solve for one of the missing functions in terms of the other. Since we already know cos(9°) = 0.6667, we can find sin(9°) as follows:

sin²(9°) = 1 - cos²(9°)

sin²(9°) = 1 - (0.6667)²

sin²(9°) = 0.5556

sin(9°) = √(0.5556) = 0.7454

3. Finding the Remaining Functions:

Once we have sin(9°) and cos(9°), we can find the other functions using their respective definitions:

sec(9°) = 1 / cos(9°) = 1 / 0.6667 = 1.5000

csc(9°) = 1 / sin(9°) = 1 / 0.7454 = 1.3416

tan(9°) = sin(9°) / cos(9°) = 0.7454 / 0.6667 = 0.8944

Therefore, the exact values of the remaining five trigonometric functions of 9° are:

sin(9°) = 0.7454

cos(9°) = 0.6667

sec(9°) = 1.5000

csc(9°) = 1.3416

tan(9°) = 0.8944