Trig Functions
Sine values are found by calculating the ratio of the length of this side to the length of the hypotenuse in a right triangle.
What is opposite?
Sine is positive in these two quadrants.
What are first and second?
Sine and cosine functions are given this name because of the repeating patterns of their graphs.
What is periodic?
What is 30 degrees?
If we know the measure of two angles in a triangle, we can find the measure of the third by using the fact that the measures of all angles in any triangle add up to this value.
What is 180?
Find the cosine value of angle A, whose opposite side has length 3, adjacent side has length 4, and hypotenuse has length 5.
What is 4/5 or 0.8?
What are first and fourth?
It's the amplitude of the function y = 10sin(3(x-2)) + 4.
What is 10?
An airplane is flying at a height of 300 meters. This is the measure (in degrees, to one decimal place) of the angle of elevation from Point A on the ground, a horizontal distance of 400 meters from the plane.
What is 36.9 degrees?
This triangle law equates the ratios of the sine of each angle to the length of its opposite side.
What is the Law of Sines?
It's the tangent value of 45 degrees.
What is 1?
Tangent is undefined at these multiples of 90 degrees.
What is odd?
It's the vertical shift of the function y = 10sin(3(x-2)) + 4.
What is 4 up?
A ship is anchored with a 30 meter long cable, which forms an angle of 39 degrees with the seabed. This is the depth (to 2 decimal places) from the ship to the seabed.
What is 18.88 meters?
SAS and SSS triangles can be solved only by using this law, similar to the Pythagorean Theorem.
What is the Law of Cosines?
The tangent value of an angle is 1/7. This is the angle's cotangent value.
What is 7?
Sine of 120 degrees has the same value as sine of this first quadrant angle.
What is 60 degrees?
It's the horizontal shift of the function y = 10sin(3(x-2)) + 4.
What is 2 right?
A radio mast is 70 meters high. A wire running from the ground to the top of the mast forms a 68 degree angle with the ground. This (to 1 decimal place) is the height of the mast.
What is 75.5 meters?
This type of incomplete triangle gets its name from the fact that it contains two known angles with one known side in between.
What are ASA triangles?
The cosine value of an angle is 4/5. This is the angle's secant value.
What is 5/4 or 1.25?
It's the value you get when you convert 30 degrees to radians.
What is pi/6?
It's the period of the function y = 10sin(3(x-2)) + 4.
What is 2pi/3?
The straight-line distance from the ground to an airplane in the air is 1,000 meters. The angle between this line and the line formed by the airplane's height is 60 degrees. This is the plane's height.
What is 500 meters?
These triangles cannot be solved because they contain no known side lengths--nor do they fix your flat tires.
What are AAA triangles?