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Cosine, Rounded

Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 23 of 52.

For $\cos\left(x\right) = 0.7$ the calculator gives arccos(0.7) = 45.57°. Cosine's partner is the mirror across the x axis, 360° − 45.57°, which is 314.43°.

A negative cosine needs no extra step: arccos already answers in quadrant II, and the partner is still 360° minus it. For cos x = −0.7, arccos gives 134.43° and the partner is 225.57°.

Challenge

A Ferris wheel of radius 10 m has its lowest point 1 m above the ground. After it turns x degrees from the bottom, a car is $h = 11-10\cos\left(x\right)$ metres up. Solve $11-10\cos\left(x\right) = 15$ for x in [0°, 360°), each to two decimal places, to find when the car is 15 m up, and press Check.

Try it yourself

11-10\cos x = 15

Get $x$ alone $0^{\circ} \le x < 360^{\circ}$

All lessons in Trig Equations and Inverses

1Your First Trig Equations

One Equation, Two Angles Reading Signs on the Circle Recap: First Equations

4Compositions

Draw the Triangle The Outer Function A Negative Inside When Undoing Does Not Undo Recap: Compositions

7General Solutions

Every Solution Tangent's Single Family Families in Radians Families, Rounded Recap: Every Solution

10Identities First

Write sin 2x Out Pick the Right cos 2x Swap cos²x for sin²x sec, csc and cot Recap: Identities First

2Inverses and Their Ranges

Why arcsin Gives One Angle The Range of arccos The Range of arctan Recap: Inverse Ranges

5Equations on a Domain

A Negative Cosine Tangent Equations Equations in Radians Two Turns, Four Answers Recap: On a Domain

8Multiple Angles

Two Turns for 2x Solving sin 2x Half Angles Every Solution of sin 3x Recap: Multiple Angles

11Final Challenges

Final: The Bicycle Pedal Final: The Big Wheel Final: Every Solution Final: An Identity and More Final: An Inverse Inside

3Evaluating Inverse Trig

Rounded Angles in Radians An Angle From a Slope Recap: Inverse Values

6Off the Special Angles

Both Answers, Rounded A Negative Sine, RoundedCosine, RoundedTangent, Rounded Rounded, in Radians Recap: Off the Table

9Factoring Trig Equations

A Common Factor Never Divide by sin x A Quadratic in Sine A Case With No Angle Square Roots Give Two Signs Recap: Factoring