Mathematics Trigonometry Quiz

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Questions and Answers

What is the reason behind using a right-angled triangle to find the height of the tree?

  • To use trigonometry and find the height of the tree (correct)
  • To use a measuring tape
  • To measure the base of the tree
  • To form a complementary angle

What is the sum of the measures of the three angles in a triangle?

  • 90°
  • 270°
  • 180° (correct)
  • 120°

What is the angle at the top of the triangle formed?

  • 30°
  • 45°
  • 90° (correct)
  • 60°

What is the name given to the side opposite the right angle in a triangle?

<p>Hypotenuse (D)</p> Signup and view all the answers

What is the relationship between the two angles in a right-angled triangle, excluding the right angle?

<p>Complementary (C)</p> Signup and view all the answers

What is the purpose of drawing a picture of the triangle?

<p>To visualize the triangle (A)</p> Signup and view all the answers

What is the condition for finding the height of the tree using a right-angled triangle?

<p>The standing place should be at a certain distance from the tree (C)</p> Signup and view all the answers

What is the purpose of using trigonometry in this problem?

<p>To find the height of the tree (C)</p> Signup and view all the answers

If sinα = 3/5, then cosα is equal to:

<p>4/5 (B)</p> Signup and view all the answers

What is the value of sin30° + cos60°?

<p>1 (C)</p> Signup and view all the answers

In the given triangle, what is the value of cosα?

<p>12/13 (D)</p> Signup and view all the answers

Which of the following are complementary angles?

<p>70° and 30° (D)</p> Signup and view all the answers

What is the value of tanα in the given triangle?

<p>12/5 (C)</p> Signup and view all the answers

What is the value of sinα in the given triangle?

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

What is the value of secα in the given triangle?

<p>13/5 (B)</p> Signup and view all the answers

Which of the following is true about sinα and cosα?

<p>Both are always less than or equal to 1 (B)</p> Signup and view all the answers

What is the value of cosecA if tan A = 4?

<p>5/4 (C)</p> Signup and view all the answers

What is the name of the trigonometric ratio that is the reciprocal of cosine?

<p>Secant (A)</p> Signup and view all the answers

What is the relationship between the trigonometric ratios and the angles of a right-angled triangle?

<p>The ratios are used to relate the angles and sides of the triangle (C)</p> Signup and view all the answers

What is the name of the trigonometric ratio that is the ratio of the opposite side to the adjacent side?

<p>Tangent (C)</p> Signup and view all the answers

Why did the teacher sing a song to introduce trigonometric ratios?

<p>To help students remember the ratios (A)</p> Signup and view all the answers

What is the name of the trigonometric ratio that is the reciprocal of sine?

<p>Cosecant (D)</p> Signup and view all the answers

What is the main concept of trigonometry?

<p>Study of angles and sides of right-angled triangles (C)</p> Signup and view all the answers

What is the purpose of learning trigonometric ratios?

<p>To solve problems involving right-angled triangles (A)</p> Signup and view all the answers

What is the value of Sinθ when θ is 30°?

<p>1/2 (D)</p> Signup and view all the answers

What is the ratio of the number of fingers above θ to the total number of fingers when calculating Cosθ?

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

What is the value of Tanθ when θ is 45°?

<p>1 (C)</p> Signup and view all the answers

What is the purpose of the Super Duper Palm?

<p>To find the values of trigonometric ratios for specific angles (C)</p> Signup and view all the answers

What is the value of Sinθ when θ is 0°?

<p>0 (D)</p> Signup and view all the answers

What is the ratio of the number of fingers below θ to the total number of fingers when calculating Sinθ?

<p>2/5 (A)</p> Signup and view all the answers

What is the value of Cosθ when θ is 90°?

<p>0 (B)</p> Signup and view all the answers

What is the ratio of the number of fingers above θ to the number of fingers below θ when calculating Tanθ?

<p>1/1 (C)</p> Signup and view all the answers

What is the relation between the angles in a right-angled triangle?

<p>Both angles are acute (A)</p> Signup and view all the answers

If sin30° = 1/2, what is the value of cos30°?

<p>√3/2 (B)</p> Signup and view all the answers

In a right-angled triangle, what is the measure of each of the acute angles?

<p>Depends on the triangle (D)</p> Signup and view all the answers

What is the value of x in the equation: x × tan45° = 1?

<p>1 (B)</p> Signup and view all the answers

What is the length of the side AB in the given figure?

<p>Cannot be determined (D)</p> Signup and view all the answers

If sinα = 1/2, what is the value of cosα?

<p>√3/2 (D)</p> Signup and view all the answers

What is the value of tan60°?

<p>√3 (B)</p> Signup and view all the answers

What is the relation between the sine and cosine of an angle?

<p>sinα = √(1 - cos²α) (D)</p> Signup and view all the answers

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Study Notes

Trigonometry Basics

  • Trigonometry deals with the relationships between the sides and angles of triangles.
  • The sum of the angles in a triangle is 180°.
  • In a right-angled triangle, one angle is 90°, and the sum of the other two angles is also 90°.

Trigonometric Ratios

  • There are six basic trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec).
  • These ratios are defined as the relationships between the sides of a right-angled triangle.

Trigonometric Identities

  • sin²A + cos²A = 1 (Pythagorean identity)
  • tanA = sinA / cosA
  • cotA = 1 / tanA
  • secA = 1 / cosA
  • cosecA = 1 / sinA

Solving Triangles

  • To solve a triangle, we need to find the values of the trigonometric ratios.
  • We can use the trigonometric identities to find the values of the ratios.

Super Duper Palm

  • The "Super Duper Palm" is a method to remember the values of trigonometric ratios for common angles (0°, 30°, 45°, 60°, and 90°).
  • The palm is divided into fingers, each representing a specific angle.
  • The values of the trigonometric ratios are marked on the fingers.

Common Angles

  • 0°: sin = 0, cos = 1, tan = 0
  • 30°: sin = 1/2, cos = √3/2, tan = 1/√3
  • 45°: sin = 1/√2, cos = 1/√2, tan = 1
  • 60°: sin = √3/2, cos = 1/2, tan = √3
  • 90°: sin = 1, cos = 0, tan = not defined

Practice Questions

  • Multiple-choice questions to practice solving triangles and finding trigonometric ratios.
  • Worksheet with questions to practice solving triangles and finding trigonometric ratios.

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