Question

Use the unit circle to evaluate the six trigonometric functions of θ = -π.

Sin θ=
Cos θ=
Tan θ=
Csc θ=
Sec θ=
Cot θ=

Answer 1

Answer:

sin=0

cos=-1

tan=0

csc=undefined

sec=-1

cot=undefined

Step-by-step explanation:

On the unit circle, $-\pi=\pi$. The sin of theta is therefore 0, the cosine is -1, and the tangent is 0/-1=0. Since the following functions are just the reciprocals of the previous ones, the cosecant is 1/0=undefined, the secant is 1/-1=-1, and the cotangent is 1/0= undefined. Hope this helps!

Answer 2

All six trigonometric ratios were calculated using a unit circle and comes out to be

$sin(-\pi )= -sin\pi =0\\cos(-\pi )= cos\pi =-1\\tan(-\pi )= -tan\pi=0 \\cosec(-\pi )= -cosec\pi =infinity\\sec(\pi )= sec\pi =-1\\cot(-\pi )=-cot\pi=infinity$

I have attached a unit circle diagram.

What is a unit circle in trigonometry?

In this unit circle corresponding values of sine and cosine have been written near the angle 'α' in form (cosα,sinα)

x-coordinate is cosα

y-coordinate is sinα

now,

one can find other trigonometric ratios

$tan\alpha =\frac{sin\alpha }{cos\alpha } \\\\cot\alpha =\frac{1}{tan\alpha } \\\\cosec\alpha =\frac{1}{sin\alpha } \\\\sec\alpha =\frac{1}{cos}$

Hence, we can find the rest of the trigonometric ratios by using the coordinates (cosα,sinα) for a particular angle 'α'.

to get more about unit circle refer to the link,

https://brainly.com/question/16577559