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Mathematics
Adriel Jones
8 June, 01:26
Sin = 5/13, and cos b = 3/5, evaluate cos (a-b).
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Mira Bray
8 June, 02:40
0
cos (a - b) is 56/65
Step-by-step explanation:
Step 1:
Given sin a = 5/13, find cos a.
sin a = opposite side/hypotenuse = 5/13
The adjacent side can be found using Pythagoras Theorem.
Hypotenuse² = Opposite Side² + Adjacent Side²
⇒ Adjacent side² = Hypotenuse² - Opposite Side²
= 13² - 5² = 169 - 25 = 144
∴ Adjacent Side = 12
⇒ cos a = adjacent side/hypotenuse = 12/13
Step 2:
Given cos b = 3/5, find sin b.
cos b = adjacent side/hypotenuse = 3/5
The opposite side can be found using Pythagoras Theorem.
Hypotenuse² = Opposite Side² + Adjacent Side²
⇒ Opposite side² = Hypotenuse² - Adjacent Side²
= 5² - 3² = 25 - 9 = 16
∴ Opposite Side = 4
⇒ sin b = opposite side/hypotenuse = 4/5
Step 3:
Find cos (a - b).
cos (a - b) = cos a cos b + sin a sin b
= 12/13 * 3/5 + 5/13 * 4/5
= 36/65 + 20/65 = 56/65
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