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Trigonometry
Question

EXAMPLE $$2$$ Evaluating Trigonometric Functions of $$45 ^ { \circ }$$

Find the values of $$\sin 45 ^ { \circ } , \cos 45 ^ { \circ }$$ , and $$\tan 45 ^ { \circ }$$ .

$$\sin ( 45 ^ { \circ } ) = \frac { \sqrt { 2 } } { 2 } ($$ Decimal: $$0.70710 \ldots )$$

Steps

$$\sin ( 45 ^ { \circ } )$$

Use the following trivial identity: $$\sin ( 45 ^ { \circ } ) = \frac { \sqrt { 2 } } { 2 }$$

$$= \frac { \sqrt { 2 } } { 2 }$$ $$\cos ( 45 ^ { \circ } ) = \frac { \sqrt { 2 } } { 2 } ($$ Decimal: $$0.70710 \ldots )$$

Steps

$$\cos ( 45 ^ { \circ } )$$

Use the following trivial identity: $$\cos ( 45 ^ { \circ } ) = \frac { \sqrt { 2 } } { 2 }$$

$$= \frac { \sqrt { 2 } } { 2 }$$ $$\tan ( 45 ^ { \circ } ) = 1$$

StepS

$$\tan ( 45 ^ { \circ } )$$

Use the following trivial identity: $$\tan ( 45 ^ { \circ } ) = 1$$

$$= 1$$

Solution
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