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What is the reciprocal of sine, and how is it calculated?
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The reciprocal of sine is cosecant (csc), calculated as 1/sin or hypotenuse/opposite.
What is the significance of the secant function in right triangle trigonometry?
Secant is the reciprocal of cosine, computed as hypotenuse/adjacent.
How is cosine used to find a side in a right triangle when given the angle and hypotenuse?
Use cos θ = adjacent/hypotenuse; solve for the adjacent side.
How do you calculate the tangent of an angle in a right triangle?
Tangent of an angle is the ratio of the opposite side to the adjacent side.
How do you determine an angle in a right triangle if you know the opposite and adjacent sides?
Use the inverse tangent function: θ = tan^(-1)(opposite/adjacent).
How does the tan inverse function help determine the angle θ with sides 5 and 4?
If tan θ = 5/4, then θ = tan^(-1)(5/4), which approximates to 51.34 degrees.
What are the special right triangle side triplets you should remember?
Remember special triplets: 3,4,5; 5,12,13; 8,15,17; 7,24,25 and their multiples.
Calculate the hypotenuse of a right triangle with legs 9 and 12.
Hypotenuse c = √(9^2 + 12^2) = √(225) = 15.
When given two sides of a right triangle, how can you find the third side?
Use the Pythagorean Theorem: if given two sides, solve for the third side using a^2 + b^2 = c^2.
What does the mnemonic SOH CAH TOA represent in trigonometry?
SOH CAH TOA helps remember trig ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
How do you identify the opposite side in a right triangle with angle θ?
The opposite side is the side directly opposite to the angle θ.
How can you solve for x using the tangent function with a given angle of 38 degrees and side 42?
Use tan θ = x/42; hence x = 42 * tan 38.
Define the cosine function in relation to a right triangle.
Cosine of an angle is the ratio of the adjacent side to the hypotenuse.
How is the Pythagorean Theorem expressed, and what is its purpose?
The theorem is expressed as a^2 + b^2 = c^2. It is used to calculate the length of a side in a right triangle.
How do you find the sine of angle θ in a right triangle with sides 3, 4, and hypotenuse 5?
Sine of θ = opposite/hypotenuse = 4/5.
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