Key to "Use the unit circle to evaluate the six..."

Chaya Galloway

Answered question

2021-08-14

Use the unit circle to evaluate the six trigonometric functions of: a)

90^{\circ}

180^{\circ}

Arham Warner

Skilled2021-08-15Added 102 answers

Given:
Use the unit circle to evaluate the six trigonometric functions:
a) 90
b) 180
Any point in on the unit circle is given by:

\Rightarrow (\cos θ, \sin θ)

a) 90:
Point on the unit circle is given by:

\Rightarrow (\cos 90, \sin 90)

\Rightarrow (0, 1)

So,

\Rightarrow \sin 90 = 1

\Rightarrow \cos 90 = 0

\Rightarrow \tan 90 = \frac{\sin 90}{\cos 90} = \frac{1}{0} = not defined

\Rightarrow \csc 90 = \frac{1}{\sin 90} = 1

\Rightarrow \sec 90 = \frac{1}{\cos 90} = not defined

\Rightarrow \cot 90 = \frac{1}{\tan 90} = 0

b) 180:
Point on the unit circle is given by:

\Rightarrow (\cos 180, \sin 180)

\Rightarrow (- 1, 0)

So,

\Rightarrow \sin 180 = 0

\Rightarrow \cos 180 = - 1

\Rightarrow \tan 180 = \frac{\sin 180}{\cos 180} = \frac{0}{- 1} = 0

\Rightarrow \csc 180 = \frac{1}{\sin 180} = not defined

\Rightarrow \sec 180 = \frac{1}{\cos 180} = - 1

\Rightarrow \cot 180 = \frac{1}{\tan 180} = not defined

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