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From The Math Page:
$$sin θ = \frac{opposite}{hypotenuse}$$ $$csc θ = \frac{hypotenuse}{opposite}$$ $$cos θ = \frac{adjacent}{hypotenuse}$$ $$sec θ = \frac{hypotenuse}{adjacent}$$ $$tan θ = \frac{opposite}{adjacent}$$ $$cot θ = \frac{adjacent}{opposite}$$
Pythagorean Identities
$$sin^2 θ + cos^2 θ = 1$$ $$1 + tan^2 θ = sec^2 θ$$ $$1 + cot^2 θ = csc^2 θ $$
A general example to help you recognize patterns and spot the information you're looking for
In a right triangle, sec θ = 4. Sketch the triangle, place the ratio numbers, and evaluate the remaining functions of θ.
To say that sec θ = 4, is to say that the hypotenuse is to the adjacent side in the ratio 4 : 1.
$$4 = \frac{4}{1}$$ To find the unknown side x, we use Pythagoras formula. $$a^2 + b^2 = c^2$$ $$x^2 + 1^2 = 4^2$$ $$x^2 + 1 = 16$$ $$x^2 = 16 - 1$$ $$x^2 = 15$$ $$x = \sqrt{15}$$
To calculate unknown values.
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