Calculus Volume 1 · free preview
Trigonometric Functions
Radian measure puts angle and arc length on the same scale, and the sine, cosine, and tangent functions, together with their reciprocal partners, describe periodic behavior through the unit circle and a small set of identities.
1. Radian measure
Radian measure
2. The trigonometric functions from the unit circle
The trigonometric functions from the unit circle
3. Graphs, period, and symmetry
Graphs, period, and symmetry
4. Fundamental identities
Fundamental identities
5. Arc length in radians
A wheel of radius 30 centimeters rotates through an angle of 2 pi/5 radians. Using s = r theta, what distance does a point on the rim travel?
6. Where the tangent is undefined
For which values of t is tan t undefined?
7. Sign of cosine in the third quadrant
Using the unit circle, what is the exact value of the cosine at 4 pi/3?
8. Period of a transformed tangent
The standard tangent has period pi. What is the period of the function f(x) = tan(2x)?
9. The Pythagorean identity
Which identity is the direct translation of the unit circle equation x^2 + y^2 = 1 into trigonometric language?
10. Degrees in a straight angle
A straight angle measures pi radians. How many degrees is that? Answer with a number.
11. Sine of pi over six
From the 30-60-90 triangle, what is the exact value of sin(pi/6)? Answer as a fraction like 1/2.
12. Range of the sine function
As the angle t varies through all real numbers, what set of values does the sine function produce?
13. Zeros of the cosine
The cosine function vanishes at the odd multiples of pi/2. What is its smallest positive zero? Answer with a number.
14. Amplitude of a shifted sine
The function f(x) = -4 sin(x) + 7 oscillates about its midline. What is its amplitude? Answer with a number.
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