Trigonometry
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Find the remaining trigonometric ratio:
Prove the identities:
Evaluate the expression:
Find all values of x in the interval [0, ] that satisfy the equation:
Graph the function:
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Solution Summary
This provides examples of working with trigonometric ratios, identities, expressions, and functions.
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Hi, herewith I have attached the solution. Please take a look at it.
Find the remaining trigonometric ratio:
Here we need to find other ratios, cos, tan, sec, csc and cot.
Given: Opposite side = 3 and hypotenuse = 5
To find the adjacent side, we have to use the Pythagorean theorem.
The adjacent side = sqrt(5^2 - 3^2)
= sqrt(25 - 9)
= sqrt(16)
= 4.
So the adjacent side = 4.
Cos ө = adj/hyp = 4/5
Tan ө = opp/adj = ¾
Sec ө = hyp/adj = 5/4
Csc ө = hyp/opp = 5/3
Cot ө = 4/3
Prove the identities:
1-
LHS = sin (pi/2 + x)
= [sin x * cos pi/2] + [cos x * sin pi/2]
Note that cos pi/2 = 0 and sin pi/2 = 1. so it becomes
= [sin x * 0] + [cos x * 1]
= 0 + cos x
= cos x
= RHS
Hence we proved left ...
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