Podcast
Questions and Answers
In a right triangle, if the side adjacent to an angle θ is 8 units and the hypotenuse is 17 units, what is the value of sin(θ)?
In a right triangle, if the side adjacent to an angle θ is 8 units and the hypotenuse is 17 units, what is the value of sin(θ)?
- 15/17 (correct)
- 8/15
- 8/17
- 17/15
A ladder leans against a wall, forming an angle of elevation of 60 degrees with the ground. If the foot of the ladder is 4 meters away from the wall, how high up the wall does the ladder reach?
A ladder leans against a wall, forming an angle of elevation of 60 degrees with the ground. If the foot of the ladder is 4 meters away from the wall, how high up the wall does the ladder reach?
- 4√3 meters (correct)
- 4 meters
- 8 meters
- 8√3 meters
Given a 30-60-90 triangle, if the side opposite the 30-degree angle is 5 units, what is the length of the hypotenuse?
Given a 30-60-90 triangle, if the side opposite the 30-degree angle is 5 units, what is the length of the hypotenuse?
- 10√3 units
- 10 units (correct)
- 5√3 units
- 5√2 units
If sin(θ) = 0.6 on the unit circle, and θ is in the second quadrant, what is the value of cos(θ)?
If sin(θ) = 0.6 on the unit circle, and θ is in the second quadrant, what is the value of cos(θ)?
Which of the following is equivalent to the expression $sec(θ) / csc(θ)$?
Which of the following is equivalent to the expression $sec(θ) / csc(θ)$?
In triangle ABC, angle A = 45°, angle B = 60°, and side a = 10 units. What is the length of side b?
In triangle ABC, angle A = 45°, angle B = 60°, and side a = 10 units. What is the length of side b?
In triangle XYZ, x = 7, y = 9, and z = 5. What is the measure of angle Z?
In triangle XYZ, x = 7, y = 9, and z = 5. What is the measure of angle Z?
What is the area of a triangle with sides of length 5, 7, and 8?
What is the area of a triangle with sides of length 5, 7, and 8?
Evaluate arcsin(1/2).
Evaluate arcsin(1/2).
What is the period of the function y = 3cos(2x)?
What is the period of the function y = 3cos(2x)?
A surveyor needs to determine the distance across a river. From a point on one bank, they measure the angle to a point on the opposite bank to be 30 degrees. They then move 50 feet along the bank and measure the angle to the same point to be 45 degrees. What is the approximate width of the river?
A surveyor needs to determine the distance across a river. From a point on one bank, they measure the angle to a point on the opposite bank to be 30 degrees. They then move 50 feet along the bank and measure the angle to the same point to be 45 degrees. What is the approximate width of the river?
Given that $tan(x) = -1$ and $sin(x) > 0$, in which quadrant does the angle x lie?
Given that $tan(x) = -1$ and $sin(x) > 0$, in which quadrant does the angle x lie?
Simplify the expression: $(sin^2(x) + cos^2(x)) / cos(x)$
Simplify the expression: $(sin^2(x) + cos^2(x)) / cos(x)$
What is the value of $cos(Ï€/2) + sin(Ï€)$?
What is the value of $cos(Ï€/2) + sin(Ï€)$?
A person stands 20 meters away from the base of a building. The angle of elevation to the top of the building is 60 degrees. What is the height of the building?
A person stands 20 meters away from the base of a building. The angle of elevation to the top of the building is 60 degrees. What is the height of the building?
Flashcards
What is Trigonometry?
What is Trigonometry?
A branch of mathematics studying relationships between triangle sides and angles.
What is the hypotenuse?
What is the hypotenuse?
The longest side of a right triangle, opposite the right angle.
What is Sine (sin)?
What is Sine (sin)?
sin(θ) = Opposite / Hypotenuse
What is Cosine (cos)?
What is Cosine (cos)?
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What is Tangent (tan)?
What is Tangent (tan)?
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What is angle of elevation?
What is angle of elevation?
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What is the Pythagorean Theorem?
What is the Pythagorean Theorem?
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What is a 45-45-90 Triangle?
What is a 45-45-90 Triangle?
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What is a 30-60-90 Triangle?
What is a 30-60-90 Triangle?
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What is the Unit Circle?
What is the Unit Circle?
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What are Quadrantal Angles?
What are Quadrantal Angles?
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What are Reciprocal Identities?
What are Reciprocal Identities?
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What is the Law of Sines?
What is the Law of Sines?
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What is the Law of Cosines?
What is the Law of Cosines?
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What are Inverse Trigonometric Functions?
What are Inverse Trigonometric Functions?
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Description
Trigonometry explores the relationships between triangle sides and angles, crucial in fields like navigation and engineering. Key concepts include right triangles, trigonometric ratios (sine, cosine, tangent). The mnemonic "SOH CAH TOA" helps remember these ratios.
