Pembahasan Soal Latihan Mandiri Trigonometri Dasar Matematika Wajib Kelas X

Summary

In this educational video, Handayani from the Math-Lab channel provides a step-by-step breakdown of 10 essential trigonometry practice problems. The video covers key concepts such as converting angles from degrees to radians, solving for trigonometric ratios like sine, cosine, and tangent, and using the Pythagorean theorem. The tutorial offers clear explanations and visual aids to help learners grasp fundamental trigonometric identities and their applications in right triangles. Viewers are encouraged to follow along and subscribe for more educational content on mathematics. The video aims to build confidence in solving basic trigonometry problems.

Takeaways

• 😀 The video focuses on solving 10 basic trigonometry problems, covering topics like conversions between degrees and radians, and using trigonometric functions.
• 😀 The first problem involves converting 150° to radians. The correct answer is 5/6π radians.
• 😀 In the second problem, 315° is converted to radians, resulting in 7/4π radians.
• 😀 Problem 3 demonstrates converting 7/6 radians to degrees, giving the result of 210°.
• 😀 Problem 4 deals with converting 9/4π radians to degrees, which equals 405°.
• 😀 In problem 5, a tan(α) = 1/7√15 leads to finding cos(α) = 7/8 using a right triangle and Pythagoras' theorem.
• 😀 Problem 6 uses tan(α) = 2/3 to find sin(α) * cos(α) = 6/13 by constructing a right triangle and applying Pythagoras' theorem.
• 😀 In problem 7, given sin(x) = t, cos(x) is derived using a right triangle, resulting in cos(x) = √(1 - t²).
• 😀 Problem 8 explores sec(θ) = 2, leading to the result of cos²(θ) - sin²(θ) = -1/2 by applying trigonometric identities.
• 😀 In problem 9, a right triangle is used to find sin(a) = 24/26 given cos(a) = 10/26, utilizing the Pythagorean theorem.
• 😀 The final problem involves calculating the length of side AC in a right triangle, where AB = 12 and cos(a) = 3/4. The result for AC is 16.

Q & A

How do you convert degrees to radians?

To convert degrees to radians, multiply the degree value by π/180. For example, to convert 150° to radians, 150 × (π/180) = 5π/6 radians.

What is the radian measure of 315°?

To convert 315° to radians, use the formula: 315 × (π/180). Simplifying, we get 7π/4 radians.

How do you convert radians to degrees?

To convert radians to degrees, multiply the radian value by 180/π. For example, to convert 7/6π radians to degrees, (7/6) × 180/π = 210°.

What is the degree measure of 9/4π radians?

To convert 9/4π radians to degrees, use the formula: (9/4π) × 180/π. This simplifies to 405°.

How do you find the value of cos(α) when tan(α) = 1/7√15?

Given tan(α) = 1/7√15, we use a right triangle. The opposite side is √15 and the adjacent side is 7. Using the Pythagorean theorem, the hypotenuse is 8. Therefore, cos(α) = adjacent/hypotenuse = 7/8.

How do you calculate sin(α) × cos(α) when tan(α) = 2/3?

For tan(α) = 2/3, we use a right triangle. The opposite side is 2, the adjacent side is 3, and the hypotenuse is √13. Therefore, sin(α) = 2/√13 and cos(α) = 3/√13. Multiplying these gives sin(α) × cos(α) = (2 × 3)/13 = 6/13.

How do you find cos(x) when sin(x) = t?

Given sin(x) = t, we use the identity sin²(x) + cos²(x) = 1. Thus, cos(x) = √(1 - t²).

What is the value of cos²(θ) - sin²(θ) when sec(θ) = 2?

Given sec(θ) = 2, cos(θ) = 1/2. Using the identity cos²(θ) - sin²(θ) = cos(2θ), we substitute cos(θ) = 1/2 and find that cos²(θ) - sin²(θ) = 1/4 - 3/4 = -1/2.

How do you calculate sin(a) if cos(a) = 10/26?

Given cos(a) = 10/26, we use the Pythagorean theorem to find the opposite side. The hypotenuse is 26 and the adjacent side is 10. Thus, sin(a) = √(26² - 10²)/26 = 24/26.

How do you find the length of side AC in a right triangle when AB = 12 and cos(A) = 3/4?

Given AB = 12 and cos(A) = 3/4, cos(A) = adjacent/hypotenuse = 12/X. Solving for X, we find X = 16. Therefore, the length of AC is 16.