40 Questions
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
What is the sum of the measures of the three angles in a triangle?
180°
What is the angle at the top of the triangle formed?
90°
What is the name given to the side opposite the right angle in a triangle?
Hypotenuse
What is the relationship between the two angles in a right-angled triangle, excluding the right angle?
Complementary
What is the purpose of drawing a picture of the triangle?
To visualize the triangle
What is the condition for finding the height of the tree using a right-angled triangle?
The standing place should be at a certain distance from the tree
What is the purpose of using trigonometry in this problem?
To find the height of the tree
If sinα = 3/5, then cosα is equal to:
4/5
What is the value of sin30° + cos60°?
1
In the given triangle, what is the value of cosα?
12/13
Which of the following are complementary angles?
70° and 30°
What is the value of tanα in the given triangle?
12/5
What is the value of sinα in the given triangle?
3/5
What is the value of secα in the given triangle?
13/5
Which of the following is true about sinα and cosα?
Both are always less than or equal to 1
What is the value of cosecA if tan A = 4?
5/4
What is the name of the trigonometric ratio that is the reciprocal of cosine?
Secant
What is the relationship between the trigonometric ratios and the angles of a right-angled triangle?
The ratios are used to relate the angles and sides of the triangle
What is the name of the trigonometric ratio that is the ratio of the opposite side to the adjacent side?
Tangent
Why did the teacher sing a song to introduce trigonometric ratios?
To help students remember the ratios
What is the name of the trigonometric ratio that is the reciprocal of sine?
Cosecant
What is the main concept of trigonometry?
Study of angles and sides of right-angled triangles
What is the purpose of learning trigonometric ratios?
To solve problems involving right-angled triangles
What is the value of Sinθ when θ is 30°?
1/2
What is the ratio of the number of fingers above θ to the total number of fingers when calculating Cosθ?
3/5
What is the value of Tanθ when θ is 45°?
1
What is the purpose of the Super Duper Palm?
To find the values of trigonometric ratios for specific angles
What is the value of Sinθ when θ is 0°?
0
What is the ratio of the number of fingers below θ to the total number of fingers when calculating Sinθ?
2/5
What is the value of Cosθ when θ is 90°?
0
What is the ratio of the number of fingers above θ to the number of fingers below θ when calculating Tanθ?
1/1
What is the relation between the angles in a right-angled triangle?
Both angles are acute
If sin30° = 1/2, what is the value of cos30°?
√3/2
In a right-angled triangle, what is the measure of each of the acute angles?
Depends on the triangle
What is the value of x in the equation: x × tan45° = 1?
1
What is the length of the side AB in the given figure?
Cannot be determined
If sinα = 1/2, what is the value of cosα?
√3/2
What is the value of tan60°?
√3
What is the relation between the sine and cosine of an angle?
sinα = √(1 - cos²α)
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.
Test your understanding of trigonometry concepts with these multiple-choice questions. Covers topics such as sine, cosine, and trigonometric identities.
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