Law of Sines
In triangle ABC, A= 40 deg, B= 60 deg, and a = 10, solve for b.
~ 13.47 or 5*sqrt(3) / sin(40 deg)
Solve for the third side, c, of a triangle where a = 5 b = 7 and <C = 45 deg.
c = 4.95
Express the reciprocal identity of csc(θ) in terms of sin(θ).
1/sin(θ)
Identify amplitude and period for f(x) = 5cos(x)
Amplitude: 5
Period: 2pi
A graph which crosses the point (0,0) in its standard form is which trig function?
f(x)=sin(x)
Acceptable answers
4/5=sin(B)
arcsin(4/5) = B
~ 53.13 deg or 126.87 deg
82.82 deg
Simplify the quotient identity expression tan(x)/sec(x) to its most basic trigonometric form.
sin(x)
Determine the period of g(x) = sin(4x)
Period: pi/2
A graph which starts at the maximum point and then descends is which kind of trig function?
f(x)=cos(x)
Solve for c in an ASA triangle where <A = 35 deg, <B = 105 deg, and b = 12.
c = 12*sin(40 deg)/ sin(105 deg)
~ 7.9 or 8
Determine the largest interior angle of a triangle with side lengths of 7cm, 8cm, and 9cm.
9cm will have the largest angle, which is 73.4 deg
Use the double angle identity for sine to rewrite the expression 10sin(x)cos(x) as a single trigonometric function.
5sin(2x)
Calculate the phase shift for h(x)=cos(x-pi/3)
Phase shift: pi/3 to the right
A graph which is the inverse of the trig function that starts at the origin and has a range of (- inf, -1] U [1, +inf) is which function?
f(x) = csc(x)
a = 10, b = 16, and A= 30 deg, how many triangles exist?
2
Calculate the length of the shorter diagonal in a parallelogram with adjacent sides of 10 and 15 units and an included angle of 60 deg.
You can choose whether or not to simplify your answer.
5sqrt(7) or sqrt(175)
True or False: (sinθ + cosθ)2=1 + sin(2θ)
True
Determine the amplitude, period, and phase shift for f(x)=3sin(2x+pi).
Amplitude: 3
Period: pi
Phase shift: -pi/2, or pi/2 to the left
A graph which has vertical asymptotes and has a range of all real numbers is which trig function?
Hint: There are two possible answers
f(x) = tan(x) or f(x) = cot(x)
A surveyor stands at Point A and measures the angle of elevation to a distant tower as 25 deg. After walking 500 meters closer to the tower to Point B, the angle of elevation is 55 deg. Use the Law of Sines to find the distance from Point B to the top of the tower.
Hint: Use supplementary angles (adds to 180 deg)
Acceptable answers
500*sin(25 deg) / (sin(30 deg))
~ 422.6 meters
An airplane flies 200 miles on a bearing of 40 deg and then turns and flies 300 miles on a bearing of 130 degrees, utilizing law of cosines, find the direct distance from the starting point to the final destination.
Hint: Add 180 to both 40 deg and subtract 130 deg from 180 to see which yields the perfect 'turn' degrees.
~ 360.5 miles
Simplify the complex synthesis sin(2x)/(1+cos(2x)) using a combination of double angle and pythagorean identities.
1+cos(2x) = 2cos2(x)
sin(2x)/2cos2(x) = tan(x)
Write a trigonometric function with a maximum value at 10, a minimum value of 2, and a period of pi, assuming no phase shift.
y= 4cos(2x)+6
What kind of graph is created when sin(x) and cos(x) are added together?
Search it up, this one's just for fun, whichever group shouts out the name first wins!
A sinusoid, which is a shifted sine wave.