trig unit 3

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What is f*g if f(x)= 1/x+2 and g(x)=x^2?

1/x^2+2

The equation cos2x = 0 has 2 solutions on the interval [0, 2ππ)

False

The equation tan5x = -3 has no solutions

False

A boat is 75 miles west and 60 miles north from the nearest port. What bearing should be taken to sail directly to port?

S 51° E

Frequency and period of simple harmonic motion are reciprocals of each other

True

Inverse sine is an odd function

True

For h(x)=x^6+x^3, find f(x) and g(x) such that h(x)=g*f(x)

f(x)=x^2, g(x)=x^3-x

Solve the equation: 2 tan^2 (x)-18=0

x = ±arctan(3) + ππn, where n is an integer.

Find the solutions of the following equation: tanx = 0

x = ππn, where n is an integer

Evaluate f*f(2)

-2

What is arctan(-√3)

-60°

Find the exact value of cos75? + cos195?

-√6/2

Evaluate f*g(1)

0

What is the period, in seconds, of the simple harmonic motion described by the equation x = 5sin(8ππt)?

0.25

What is f*g if f(x)=1/x+2 and g(x)=x^2?

1/x^2+2

Write cos(arctan(x)) as an algebraic expression

1/√x^2+1

For f(x)=2/x-3, find f^1(x)

120°

A handicap-accessible entrance to a building is 6 feet above the ground and is connected to the ground level parking lot by a ramp. If the length of the ramp is 25 feet, what angle does the ramp make with the ground?

14°

Find the exact value of cos^-1(tan 135°)

180°

Find the exact value of sin (cos^-1(1/3))

2 √2/3

A plane is 180 miles south and 95 miles east of the airport. What bearing should be taken to fly directly to the airport?

332°

In an isosceles triangle, the equal sides are 10 and the altitude dropped to the base is 6. Find approximate degree measures of all the angles in the triangle

37°, 37°, 106°

n an isosceles triangle, the equal sides are 10 and the altitude dropped to the base is 6. Find approximate degree measures of all the angles in the triangle.

37°, 37°, 106°

Find all solutions of the following equation: tan(1/4x)=10

4arctan(10) + 4ππn, where n is an integer

Find a model for simple harmonic motion with amplitude 5 cm and period of 0.5 seconds, such that the displacement is 0 when t = 0

5sin(4ππt)

Angular frequency equals frequency divided by 2π2π

False

Arctan(tan(105°)) = 105°

False

Composition of secant and cosine is an identity

False

Functions f(x)=^4√x+3 and g(x)=(x-3)^4 are interses of each other

False

If in the equation tanx = a the value of a is negative, then x is also negative

False

Inverse cosine is an even function

False

Simple harmonic motion can be modeled by any periodic function

False

The arctangent function is a ratio of the arcsine function to the arccosine function

False

The composition functions f?g and g?f are equal to each other for any f and g

False

The domain inverse tangent is [−π2,π2]

False

The equation tan^2(x)-25=0 has 2 solutions on the interval [0,2π)

False

The function given as the following set of ordered pairs is invertible:{(-7, 1) ,(-3, 4), (1, 9), (5, 4) (9, -1)

False

The product of two sine functions equals the sine of the product

False

The range of inverse cosine includes some negative numbers

False

The sum of the cosines equals the cosine of the sum

False

Amplitude is the maximum displacement of the object in simple harmonic motion

True

Arccos(cos(-25°)) = 25°

True

Function f(x)=2 √x-3 +5 is invertible

True

If f(x) = x, then f?g = g?f for any g(x)

True

In a right triangle, it is sufficient to know the lengths of any two sides to determine all the angles and the length of the third side

True

In air navigation, bearing is an angle measured in clockwise direction from the line pointing north to the path of the plane or a line of sight

True

In marine navigation and surveying, the degree measure of a bearing can have any value between 0° and 90°

True

The equation 3cot^2 (x)+1=0 has no solutions

True

The equation sec2x - 2 = 0 has 4 solutions on the interval [0, 2π)

True

The equation sin^2(x)-sin x-12=0 has no solutions

True

The expression 2sin3xsin9x equals to

cos6x - cos12x

The expression 2cos2xcos6x equals to

cos8x + cos4x

For f(x)=x^3+1, find f^1(x)

f^-1 (x)=^3√x-1

The expression 2sin5xcos7x equals to

sin12x - sin2x

Evaluate g*f(1)

undefined

What is arcsin (π/2)?

undefined

What is g*f if f(x) = √x-1 and g(x) = x^2+2

x + 1

Find all solutions of the following equation: sin(1/3x) =-√3/2

x = -ππ + 6ππn and x = 4ππ + 6ππn, where n is an integer

Find all solutions of the equation tan^2 x-tan x-6=0 on the interval [0,2π)

x = arctan(3), x = ππ + arctan(3), x = 2ππ -arctan(2), x = ππ - arctan(2)

Solve the equation: 4sin^2 (x)-1=0

x=+π/6+πn

Find the solutions of the following equation: √2csc x +2=0

x=-π/4 + 2πn and x=5π/4 +2πn, where n is an integer

Find the solutions of the following equation: sin2x = 0

x=π/2n, where n is an integer

What is arccos(-1)?

ππ

Find the exact value of cos(arctan(-2))

√5/5


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