Question

Let 0°
Given: tan a =2.4

Find: sin a and cos a

Answer 1

• sin α = 12/13;
• cos α = 5/13.

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Since angle α is between 0° and 90°, it is in the first quadrant and therefore all sin α, cos α and tan α are positive numbers.

Use the following identities:

• tan α = sin α / cos α;
• sin² α + cos² α = 1.

Given tan α = 2.4. Using identities, find cosine as follows:

• sin α / cos α = 2.4
• sin α = 2.4 cos α

• cos² α = 1 - sin² α
• cos² α = 1 - (2.4 cos² α)²
• cos² α = 1 - 5.76 cos² α
• cos² α + 5.76 cos² α = 1
• 6.76 cos² α = 1
• 2.6 cos α = 1
• cos α = 1/2.6
• cos α = 10/26
• cos α = 5/13

Find sine:

• sin² α = 1 - cos² α
• sin² α = 1 - (5/13)²
• sin² α = 1 - 25/169
• sin² α = 144/169
• sin α = 12/13