Question about Trigonometric Lines of 75º, 15º, 22.5º
Subject Mathematics
Mathematics
Source Originais Teachy
Originais Teachy
Topic Trigonometric Lines of 75º, 15º, 22.5º
Trigonometric Lines of 75º, 15º, 22.5º
Difficulty Hard
Hard
(Originais Teachy 2024) - Question Hard of Mathematics
During the cleaning of the cooling system of a factory, a technician must adjust a light reflector fixed on the ceiling of the room. The reflector has the shape of a right circular cone with the vertex pointing upwards and an opening angle of 75º. The technician wants to calculate the height and the radius of the base of the cone to determine the ideal dimensions of the mirrors that will be installed on the inner surface of the cone, so that the reflected light follows a beam parallel to the floor. Consider that the angle of incidence of light on the inner surface of the cone should be 15º with the normal to the surface at the point of incidence to ensure total reflection of light. Based on this configuration, determine the height and the radius of the base of the cone, and additionally, identify the value of the sine and cosine of 22.5º, an angle that arises in the resolution of the problem.a.
Height h ≈ 0.0927 and base radius r ≈ 0.1392. Sine of 22.5º ≈ 0.6614 and cosine of 52.5º ≈ 0.5000.
b.
Height h ≈ 0.1392 and base radius r ≈ 0.0927. Sine of 22.5º ≈ 0.6614 and cosine of 52.5º ≈ 0.5000.
c.
Height h ≈ 0.0927 and base radius r ≈ 0.1392. Sine of 22.5º ≈ 0.5000 and cosine of 52.5º ≈ 0.6614.
d.
Height h ≈ 0.1392 and base radius r ≈ 0.0927. Sine of 22.5º ≈ 0.5000 and cosine of 52.5º ≈ 0.6614.
e.
Height h ≈ 0.1392 and base radius r ≈ 0.0927. Sine of 22.5º ≈ 0.6614 and cosine of 52.5º ≈ 0.5000.
Answer sheet:
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Curabitur id consequat justo. Cras pellentesque urna ante, eget gravida quam pretium ut. Praesent aliquam nibh faucibus ligula placerat, eget pulvinar velit gravida. Nam sollicitudin pretium elit a feugiat. Vestibulum pharetra, sem quis tempor volutpat, magna diam tincidunt enim, in ullamcorper tellus nibh vitae turpis. In egestas convallis ultrices. Sed non sem ultricies, sollicitudin sem facilisis, commodo justo. Maecenas mattis sodales nunc, et auctor massa fermentum a. Maecenas eget nisl felis.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Curabitur id consequat justo. Cras pellentesque urna ante, eget gravida quam pretium ut. Praesent aliquam nibh faucibus ligula placerat, eget pulvinar velit gravida. Nam sollicitudin pretium elit a feugiat. Vestibulum pharetra, sem quis tempor volutpat, magna diam tincidunt enim, in ullamcorper tellus nibh vitae turpis. In egestas convallis ultrices.
Answer sheet
You need to be a registered teacher to view the answer sheet
IARA TIP
Are you putting together a test or exercise list?
On Teachy’s platform, you can automatically generate these materials without spending hours searching for questions 😉
Those who viewed this question also liked...
Question
Question
Difficulty Hard
Source:
ENEM
Sequence Terms
Difficulty Hard
Question
Question
Difficulty Medium
Source:
Teachy
João wishes to save a certain amount of money every month, and for that, he established a sequence in which the saved amount increases gradually. In the first month, João saved R$ 100.00. In the second month, he saved R$ 120.00, and in the third month, R$ 140.00. Considering that this sequence is arithmetic, (a) determine the reason for this sequence; (b) find the amount that João will save in the fifth month; and (c) calculate the total amount saved by João after the first six months.
Elements of a Sequence
Difficulty Medium
Question
Question
Difficulty Hard
Source:
Teachy
In Ana's lunchbox, she has 8 green grapes and 6 purple grapes. In João's lunchbox, he has 4 grapes of each color. If they combine all the grapes and divide them equally between them, who will have more grapes, Ana or João? Write two different addition equations that result in the same total number of grapes to help Ana and João divide the grapes fairly.
Equality: Identical Sums and Subtractions
Difficulty Hard
Question
Question
Difficulty Easy
Source:
Teachy
Imagine you have 432 candies and want to separate them into containers of 100, 10, and individual units to facilitate counting. How would you make this separation? Explain your answer by showing how the number 432 can be decomposed into powers of 10.
Composition and Decomposition of Natural Numbers into Powers of 10
Difficulty Easy
Join a community of teachers directly on WhatsApp
Connect with other teachers, receive and share materials, tips, training, and much more!
We reinvent teachers' lives with artificial intelligence
Materials
2023 - All rights reserved