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Property 4

Definition of the Trigonometric Functions (Right Triangle)

c is the hypotenuse; b is opposite α; a is adjacent to α.

\(\cos\alpha=\samefrac{\text{Length of adjacent}}{\text{Length of hypotenuse}}=\samefrac ac\)
\(\sin\alpha=\samefrac{\text{Length of opposite}}{\text{Length of hypotenuse}}=\samefrac bc\)
\(\tan\alpha=\samefrac{\text{Length of opposite}}{\text{Length of adjacent}}=\samefrac ba\)
\(\cot\alpha=\samefrac{\text{Length of adjacent}}{\text{Length of opposite}}=\samefrac ab\)

Example

\(\sin\alpha=\samefrac35\)
\(\cos\alpha=\samefrac45\)
\(\tan\alpha=\samefrac34\)
\(\cot\alpha=\samefrac43\)

Find the trigonometric values of the angles of the right triangles below.

1.
\(\sin\alpha=?\)
\(\cos\alpha=?\)
\(\tan\alpha=?\)
\(\cot\alpha=?\)
2.
\(\sin\alpha=?\)
\(\cos\alpha=?\)
\(\tan\alpha=?\)
\(\cot\alpha=?\)
3.
\(\sin\alpha=?\)
\(\cos\alpha=?\)
\(\tan\alpha=?\)
\(\cot\alpha=?\)
4.
\(\sin\alpha=?\)
\(\cos\alpha=?\)
\(\tan\alpha=?\)
\(\cot\alpha=?\)
\(\sin\beta=?\)
\(\cos\beta=?\)
\(\tan\beta=?\)
\(\cot\beta=?\)