Inverse Cosine
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 24 of 50.
Every ratio has its inverse. When you know the adjacent side and the hypotenuse, the cosine links them, and arccos gives the angle back.
A rope 7 m long is pegged 4 m from the foot of a pole. The 4 m along the ground touches the angle at the peg, so cos(theta) = 4/7, and theta = acos(4/7), about 55.15°. That is the angle the rope makes with the ground.
The cosine shrinks as the angle grows: a cosine near 1 means a flat angle, a cosine near 0 an angle near 90°. 4/7 is a little more than a half, and cos 60° is exactly a half, so the angle should be a little under 60°. It is.
Challenge
Triangle PQR has a right angle at P. For the angle θ at Q, the adjacent side is 9 and the hypotenuse is 13. Find θ in degrees, rounded to two decimal places. Then press Check.
Try it yourself
Use the figure to find theta
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Right-Triangle Trigonometry
1Sides of a Right Triangle
How Tall Is the Tree?The HypotenuseThe Opposite SideThe Adjacent SideWhen the Angle MovesRecap: Naming the Sides2The Three Ratios
The Sine RatioThe Cosine RatioThe Tangent RatioChoosing the RatioRecap: The Three Ratios5Finding an Angle
Inverse SineInverse CosineInverse TangentThe Angle of a RampBoth Acute AnglesRecap: Finding an Angle