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A Negative Sine, Rounded

Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 22 of 52.

For $\sin\left(x\right) = -0.3$ the calculator says arcsin(−0.3) = −17.46°. That is a real answer, but outside [0°, 360°): add 360° and it is 342.54°.

The mirror across the y axis is 180° − (−17.46°), which is 197.46°. Both points are below the x axis, in quadrants III and IV, where a negative sine belongs. Students often drop −17.46° as "wrong" and lose an answer.

Challenge

Solve $5\sin\left(x\right)+3 = 0$ for every x in [0°, 360°), each to two decimal places, and press Check.

Try it yourself

5\sin x+3 = 0

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, RoundedA Negative Sine, RoundedCosine, Rounded Tangent, 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