Math: Trigonometry
Trig functions, identities, unit circle, and triangle solving.
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What ratio does the sine function represent in a right triangle according to SOH-CAH-TOA?
The sine function represents the ratio of the length of the opposite side to the length of the hypotenuse.
What is the formula to convert an angle from degrees to radians?
To convert degrees to radians, multiply the angle by π / 180.
What is the exact value of sin(30°) on the unit circle?
The exact value of sin(30°) is 1/2.
Which primary trigonometric function is the reciprocal of the secant function (sec)?
The cosine function (cos) is the reciprocal of the secant function.
What is the fundamental Pythagorean trigonometric identity involving sine and cosine?
The fundamental Pythagorean identity is sin²(θ) + cos²(θ) = 1.
In the trigonometric graph y = A sin(Bx - C) + D, what does the absolute value of 'A' represent?
The absolute value of 'A' represents the amplitude, which is the maximum displacement from the midline.
What is the exact value of cos(45°) or cos(π/4)?
The exact value of cos(45°) is √2 / 2.
Why is the value of tan(90°) considered undefined?
The value of tan(90°) is undefined because tangent is sine divided by cosine, and cos(90°) is 0, making division by zero impossible.
How is the cotangent function (cot) expressed in terms of sine and cosine?
The cotangent function is expressed as cos(θ) / sin(θ).
What is the Pythagorean identity that relates the tangent and secant functions?
The Pythagorean identity relating tangent and secant is 1 + tan²(θ) = sec²(θ).
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