Solving Trig Equations
The solution(s) to the equation 2sin(t)-1=0 when 0≤t<2π
What are t=π/6 or t=5π/6?
The maximum and minimum values of the sine graph.
What are 1 and -1?
The mnemonic device used to remember the basic trig ratios for a right triangle.
What is SOH-CAH-TOA?
This law is used to solve triangles when you know two angles and one side (ASA or AAS) or two sides and an angle not between them (SSA).
What is the Law of Sines?
This is the formula for sin(u+v).
What is sin(u)cos(v)+cos(u)sin(v)?
The general solution for cos(x)=0
What is x=π/2±πn?
The length of one full cycle of the function f(x)=4sin(x)
What is the period, 2π?
The length of the missing side, b, if a=6 and c=10 in a right triangle where c is the hypotenuse.
What is b=8?
For a triangle with sides a, b, and c, this is one form of the Law of Cosines used to find side c.
What is c2 = a2 +b2 - 2ab(cos(C))
The formula for cos(2x) in terms of cos(x) and sin(x)?
What is cos2(x)-sin2(x) or 2cos2(x)-1 or 1-2sin2(x)
The solutions for tan2(x)=1 in the interval 0≤x<π
What are x=π/4 or x=3π/4?
The amplitude of the function f(x)=1/2 cos(x), and the type of transformation of the parent curve it results in.
What is an amplitude of 1/2, which vertically shrinks the curve?
The height of a tree if the sun is 62 degrees above the horizon and the tree casts a shadow that is 12 feet long.
What is 12•sin(62°) feet, approximately 78.8 feet?
In Triangle ABC, m<A=30°, m<B=45°, and side a=10. Find the length of side b (either exact length or approximate, rounded to the nearest hundredth)
What is b=10root(2) or approximately 14.14?
The formula for sin(2x).
What is 2sin(x)cos(x)?
The solutions for 2sin2(x)+sin(x)-1=0, in the interval [0,2π).
What are x=π/6, x=5π/6, and x=3π/2?
The period of the function f(x)=cos(π/8 x).
What is 16?
Given a right triangle with legs a=5 and b=12, find the value of sin(A)
What is 5/13?
In triangle ABC with side lengths a=3, b=4, and c=6, this is the measure of angle C rounded to the nearest degree.
What is approximately 117°?
The exact value of cos(75°).
What is [root(6) - root(2)] / 4 ?
The solutions for cos(2x)=1/2
What are x=π/6, x=5π/6, x=7π/6, and x=11π/6?
A sine function with amplitude 3, period π, phase shift left π/8, and vertical shift down 4.
What is y=3sin(2(x+π/8))-4?
The angle of elevation to the top of a tree is 9° from a point 125 feet away from the base. How tall is the tree to the nearest tenth of a foot if the observer's eye level is 6 feet above the ground?
What is approximately 25.8 feet?
A baseball diamond has 90-foot sides. The pitcher's mound is 60.5 feet from home plate. This is the distance from the pitcher's mound to third base (to the nearest tenth of a foot).
What is approximately 63.7 feet?
Given sin(θ) = 3/5, 0°≤θ≤90°. This is the exact value of cos(2θ).
What is 7/25?