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
