Question

Find the values of the six trigonometric functions for angle G.

Answer 1

Answers:

• sin(G) = 3/5
• cos(G) = 4/5
• tan(G) = 3/4
• csc(G) = 5/3
• sec(G) = 5/4
• cot(G) = 4/3

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Explanation:

For a right triangle, the sine of a reference angle is equal to the opposite over hypotenuse.

sin(angle) = opposite/hypotenuse

cosine involves adjacent over hypotenuse

cos(angle) = adjacent/hypotenuse

tangent involves opposite over adjacent

tan(angle) = opposite/hypotenuse

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In short, we have this list so far

• sin(angle) = opposite/hypotenuse
• cos(angle) = adjacent/hypotenuse
• tan(angle) = opposite/hypotenuse

The other three trig functions are reciprocals of these first three. Cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent.

Meaning, the other three trig ratios are

• csc(angle) = hypotenuse/opposite
• sec(angle) = hypotenuse/adjacent
• cot(angle) = adjacent/opposite

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So,

• sin(G) = opposite/hypotenuse = FH/FG = 24/40 = 3/5
• cos(G) = adjacent/hypotenuse = GH/FG = 32/40 = 4/5
• tan(G) = opposite/adjacent = FH/GH = 24/32 = 3/4

and

• csc(G) = hypotenuse/opposite = FG/FH = 40/24 = 5/3
• sec(G) = hypotenuse/adjacent = FG/GH = 40/32 = 5/4
• cot(G) = adjacent/opposite = GH/FH = 32/24 = 4/3

Answer 2

Answer:

Step-by-step explanation:

Hope this helps u!!