Gr 11 Math Ch 6: Area, Sine and Cosine Rules
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Questions and Answers

What is the formula for the area of a triangle using the Area Rule?

  • $\frac{1}{2} ab \sin C$
  • $\frac{1}{2} bc \sin A$ (correct)
  • $bc \sin A$
  • $\frac{1}{2} bc \cos A$

    • When should you use the Sine Rule?

  • When you know two angles and the included side.
  • When you know three sides.
  • When you know two sides and a non-included angle. (correct)
  • When you know two sides and the included angle.

    • What is the formula for the Cosine Rule?

  • $a^2 = b^2 + c^2 + 2bc \cos A$
  • $a^2 = b^2 - c^2 + 2bc \cos A$
  • $a^2 = b^2 + c^2 - bc \cos A$
  • $a^2 = b^2 + c^2 - 2bc \cos A$ (correct)

    • In which quadrant is the tangent function positive?

    <p>Quadrant III</p> Signup and view all the answers

    What is the condition for using the Cosine Rule?

    <p>Two sides and the included angle are given.</p> Signup and view all the answers

    When can you use the Area Rule?

    <p>When no perpendicular height is given.</p> Signup and view all the answers

    What is the purpose of the CAST diagram?

    <p>To remember the signs of trigonometric functions in different quadrants.</p> Signup and view all the answers

    What is a general solution of a trigonometric equation?

    <p>A solution that takes into account the periodic nature of the trigonometric functions.</p> Signup and view all the answers

    What is the main difference between the Sine Rule and the Cosine Rule?

    <p>The Sine Rule is used for solving triangles with two sides and a non-included angle, while the Cosine Rule is used for solving triangles with two sides and the included angle.</p> Signup and view all the answers

    If you are given two sides and the included angle of a triangle, which rule should you use to solve the triangle?

    <p>The Cosine Rule</p> Signup and view all the answers

    In which quadrant is the cosine function positive?

    <p>Quadrant IV</p> Signup and view all the answers

    What is the purpose of the CAST diagram in trigonometry?

    <p>To represent the signs of trigonometric functions in different quadrants</p> Signup and view all the answers

    If you are given two angles and a side of a triangle, which rule should you use to solve the triangle?

    <p>The Sine Rule</p> Signup and view all the answers

    What is the main difference between the Area Rule and the other two trigonometric rules?

    <p>The Area Rule is used for finding the area of a triangle, while the other two rules are used for finding the lengths of sides and the measures of angles.</p> Signup and view all the answers

    If you are given three sides of a triangle, which rule should you use to solve the triangle?

    <p>The Cosine Rule</p> Signup and view all the answers

    What is the characteristic of a general solution to a trigonometric equation?

    <p>It takes into account the periodic nature of the trigonometric functions</p> Signup and view all the answers

    What is the condition for using the Area Rule?

    <p>When no perpendicular height is given</p> Signup and view all the answers

    In which quadrants are the sine and cosine functions positive?

    <p>Quadrant I and Quadrant IV</p> Signup and view all the answers

    What is the characteristic of the Sine Rule?

    <p>It is used when no right angle is given</p> Signup and view all the answers

    What is the purpose of the CAST diagram?

    <p>To identify the trigonometric functions that are positive in each quadrant</p> Signup and view all the answers

    When can you use the Cosine Rule?

    <p>When three sides are given</p> Signup and view all the answers

    What is the main difference between the Area Rule and the other two trigonometric rules?

    <p>It is used to find the area of a triangle</p> Signup and view all the answers

    What is the condition for using the Sine Rule?

    <p>When two angles and a side are given</p> Signup and view all the answers

    What is the formula for the area of a triangle using the Area Rule, when two sides and the included angle are given?

    <p>All of the above</p> Signup and view all the answers

    If a triangle has two sides of length 5 and 7, and the angle between them is 60°, which rule would be used to find the length of the third side?

    <p>Cosine Rule</p> Signup and view all the answers

    In which quadrant is the value of sin(x) equal to the value of cos(x)?

    <p>Quadrant II</p> Signup and view all the answers

    What is the general solution to the equation sin(x) = 1/2?

    <p>x = 30° + 360°k</p> Signup and view all the answers

    If a triangle has two angles of 30° and 60°, and one side of length 5, which rule would be used to find the length of the other two sides?

    <p>Sine Rule</p> Signup and view all the answers

    What is the value of cos(A) in a triangle with sides of length 3, 4, and 5, and angle A opposite the side of length 4?

    <p>3/5</p> Signup and view all the answers

    In which quadrant(s) is the value of tan(x) negative?

    <p>Quadrant II and IV</p> Signup and view all the answers

    What is the value of sin(B) in a triangle with sides of length 5, 7, and 8, and angle B opposite the side of length 7?

    <p>7/8</p> Signup and view all the answers

    If a triangle has three sides of length 5, 7, and 8, which rule would be used to find one of its angles?

    <p>Cosine Rule</p> Signup and view all the answers

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