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Advanced Math/trig study guide,(im clueless)
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Question
Evaluate the sine, cosine, and tangent of the real number t = 7π/4.
Find the exact value of tan 21π using periodic properties.
2 4
1 0
4. Evaluate cos 2π without using a calculator.
1 0
-1 undefined
5. Evaluate sin 4π without using a calculator.
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-1 1
6. Evaluate sin π without using a calculator.
-1 1
undefined 0
For what values of x is the graph of y = sin x increasing from 0 to 1, when -π ≤ x ≤ π?
8. It is easiest to graph y = sec x by first sketching the graph of what function?
9. The graph of y = tan x is symmetric with respect to _____.
10. Which equation of a sine function has the following characteristics: amplitude = 1, period = 3π? y = sin x
Find the exact value of tan 21π using periodic properties.
The trig function has period 2π. Since 21π is π over 20π,
the solution would be found by finding what tan(π) was.
It is known that this is 0.
4. Evaluate cos 2π without using a calculator.
2π is the same as 0, but the calculator will just know it is close to 2π,
so the answer will be close to 0.
5. Evaluate sin 4π without using a calculator.
Since by period 2π, that is the same as sin 0, it is known to b e0.
6. Evaluate sin π without using a calculator.
The sin wave is known to come back to 0 on every integer multiple of π,
so sin π = 0 as well.
7. For what values of x is the graph of y = sin x increasing from 0 to 1, when -π ≤ x ≤ π?
It is known that sin(0) = 0 and sin(π) = 1, so the interval is from 0 to π.
8. It is easiest to graph y = sec x by first sketching the graph of what function?
For me, the easiest way is to know that y = 1/(cos x),
so first sketch the cos x curve and then find the inverse at each point.
9. The graph of y = tan x is symmetric with respect to _____.
y = ctn x since tan x = sin x / cos x and ctn x = cos x / sin x.
10. Which equation of a sine function has the following characteristics:
amplitude = 1, period = 3π?
y = sin x has amplitude 2 and range 2π. Since we want amplitude 1, divide by 2 and get
y = (sin x)/2. Since the period is 2π and we want period 3π, multiply x by 2/3.
This gives y = [sin(3x/2)] / 2.
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Scott A Wilson
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