Gr 10 Math Ch 4: Solving Trigonometric Equations

What is the first step in solving a trigonometric equation?

Use a calculator to find the angle

Identify the trigonometric ratio involved (correct)

Rearrange the equation to isolate the trigonometric ratio

Determine if there is a solution

When can there be no solution for a trigonometric equation?

When the ratio exceeds 1 for sine or cosine

When the triangle is not right-angled

When the values are outside the domains of the trigonometric functions (correct)

When the angle is negative

Which inverse trigonometric function would you use to find an angle if the sine ratio is known?

tan⁻¹

cos⁻¹

cosec⁻¹

sin⁻¹ (correct)

To find unknown lengths in right-angled triangles, which trigonometric ratios can be used?

Sine, cosine, and tangent Signup and view all the answers

If two sides of a right-angled triangle are known, which can be calculated next?

The angles of the triangle using trigonometric ratios Signup and view all the answers

What must be done after rearranging a trigonometric equation?

Use a calculator to find the angle Signup and view all the answers

What is the first action you should take when starting to solve a trigonometric equation?

Identify the trigonometric ratio involved. Signup and view all the answers

Which scenario would indicate that a trigonometric equation might have no solution?

The sine ratio is greater than 1. Signup and view all the answers

What must be calculated using trigonometric ratios when two sides of a right-angled triangle are known?

The angles inside the triangle. Signup and view all the answers

In solving trigonometric equations, which function is used to find an angle from the cosine ratio?

cos^-1 Signup and view all the answers

What is the correct procedure after isolating the trigonometric ratio in an equation?

Use an inverse trigonometric function to find the angle. Signup and view all the answers

Which trigonometric function would be used to solve for an angle if the tangent ratio is known?

tan^-1 Signup and view all the answers

What is the consequence of trying to find an angle using a sine ratio greater than 1?

There may be no solution as it exceeds the sine function's range. Signup and view all the answers

Which of the following statements is accurate regarding the use of inverse trigonometric functions?

Inverse functions give a specific angle even if multiple angles are valid solutions. Signup and view all the answers

Which process is NOT part of solving a trigonometric equation?

Perform an approximation of the angle. Signup and view all the answers

What is a critical consideration when rearranging trigonometric equations for calculation?

The equality of the original equation must be maintained through proper alteration. Signup and view all the answers

When isolating a cosine ratio in an equation, which representation is essential to consider?

The ratio must remain within the limits of negative one and positive one. Signup and view all the answers

What might indicate that a trigonometric problem can only yield complex solutions?

Having sides of a triangle that violate the triangle inequality theorem. Signup and view all the answers