Mid-Chapter Quiz
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Identify the hypotenuse as well as the adjacent and opposite sides of the angle. Use the Pythagorean Theorem to find the missing side length.
sin θ=sqrt(7)/4, cos θ=3/4, tan θ=sqrt(7)/3, csc θ=4sqrt(7)/7, sec θ=4/3, cot θ=3sqrt(7)/7
In a right triangle the hypotenuse is the side that is opposite the right angle. If we take one of the acute angles as a reference, we can identify the opposite and adjacent sides to the angle.
Let's find the values of the six trigonometric functions for angle θ. Remember to rationalize denominators if needed.
| Function | Substitute | Simplify |
|---|---|---|
| sin θ=opp/hyp | sin θ=3sqrt(7)/12 | sin θ=sqrt(7)/4 |
| cos θ=adj/hyp | cos θ=9/12 | cos θ=3/4 |
| tan θ=opp/adj | tan θ=3sqrt(7)/9 | tan θ=sqrt(7)/3 |
| csc θ=hyp/opp | csc θ=12/3sqrt(7) | csc θ=4sqrt(7)/7 |
| sec θ=hyp/adj | sec θ=12/9 | sec θ=4/3 |
| cot θ=adj/opp | cot θ=9/3sqrt(7) | cot θ=3sqrt(7)/7 |
a/b=.a /3./.b /3.
a/b=a * sqrt(7)/b * sqrt(7)
a* a=a^2
( sqrt(a) )^2 = a
a/b=.a /3./.b /3.
a/b=a * sqrt(7)/b * sqrt(7)
a* a=a^2
( sqrt(a) )^2 = a