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Trigonometric functions
- Find the angle I
- Find the angle II
- Find the angle III
Trigonometric functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle.
If we have a right triangle with one angle \(\theta\)
Then the following hold true
$$sine\: \theta =\frac{a}{c}$$
$$cosine \:\theta =\frac{b}{c}$$
$$tangent \:\theta =\frac{a}{b}$$
$$cosecant \:\theta =\frac{c}{a}$$
$$secant \:\theta =\frac{c}{b}$$
$$cotangent \:\theta =\frac{b}{a}$$
If we are given one angle in a right triangle \( \theta = 45^{\circ}\) and we know that the measure of the hypotenuse is 2, what are the measures of the two other legs?
Using the formulas above we get that:
$$sine\; 45^{\circ}=\frac{a}{2}$$
$$cosine\; 45^{\circ}=\frac{b}{2}$$
We use our calculators to determine sine \(45^{\circ}\) and cosine \(45^{\circ}\) :
$$0.707=\frac{a}{2}$$
$$0.707=\frac{b}{2}$$
Now we can see that the measures of \(a\) and \(b\) are equal and that the length is
$$2 \cdot 0.707 = 1.414$$
Video lesson
If we are given one angle in a right triangle \(\theta = 20^{\circ}\) and we know that the measure of the hypotenuse is 3, what are the measures of the two other legs?
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Kuta Software - Infinite Algebra 2. Right Triangle Trig. - Evaluating Trig. Ratios. Find the value of the trig function indicated.
Worksheet by Kuta Software LLC. Kuta Software - Infinite Algebra 2 ... Find the value of the trig function indicated. 1) sec θ. 17. 8. 15 θ. 2) sec θ.
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Worksheet by Kuta Software LLC. Use the given point on the terminal side of angle θ to find the value of the trigonometric function indicated. 23) sin θ.
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Trigonometric functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle.
Find the value of the trig function indicated. 22) tan q. 13. 5 q. 23) tan q. 20.
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