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Algebra 1
Found in: Page 661
Algebra 1

Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801

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Short Answer

Find the values of the three trigonometric ratios of A.

The three trigonometric ratios of A are as follows.

role="math" localid="1647948666906" sinA=45cosA=35tanA=43

See the step by step solution

Step by Step Solution

Step 1. Define the three trigonometric ratios.

If θ is any angle in a given right angle triangle, then the three trignometric ratios are,

sinθ=length  of  side  opposite  to  θ   length  of  hypotenusecosθ=length  of  side  adjacent  to  θ   length  of  hypotenusetanθ=length  of  side  opposite  to  θength  of  side  adjacent  to  θ  

Step 2. Calculate the value of three trigonometric ratios of angle A.

Observe the figure.

From the figure, AB is hypotenuse (side opposite to 90 degree) and length of AB is 5 units.

CB is the side opposite to angle A and length of CB is 4 units.

AC is the side adjacent to angle A and length of AC is 3 units.

sinA=length  of  side  opposite  to  A   length  of  hypotenuse=length  of  CBlength  of  hypotenuse=45cosA=length  of  side  adjacent  to  A   length  of  hypotenuse=length  of  AClength  of  hypotenuse=35tanA=length  of  side  opposite  to  Alength  of  side  adjacent  to  A  =length  of  CBlength  of  AC=43

Step 3. State the conclusion.

The three trigonometric ratios are sinA,cosA, tanAand their values are as follows.

sinA=45cosA=35tanA=43

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