How do you do this question?
1 answer:
Answer:
Correct integral, third graph
Step-by-step explanation:
Assuming that your answer was 'tan³(θ)/3 + C,' you have the right integral. We would have to solve for the integral using u-substitution. Let's start.
Given : ∫ tan²(θ)sec²(θ)dθ
Applying u-substitution : u = tan(θ),
=> ∫ u²du
Apply the power rule ' ∫ xᵃdx = x^(a+1)/a+1 ' : u^(2+1)/ 2+1
Substitute back u = tan(θ) : tan^2+1(θ)/2+1
Simplify : 1/3tan³(θ)
Hence the integral ' ∫ tan²(θ)sec²(θ)dθ ' = ' 1/3tan³(θ). ' Your solution was rewritten in a different format, but it was the same answer. Now let's move on to the graphing portion. The attachment represents F(θ). f(θ) is an upward facing parabola, so your graph will be the third one.
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The value for y is 17.5°
The equation is
Sin (3y - 30°) = Cos (7y +50°)
<h3>What is Trigonometry ?</h3>Trigonometry is the branch oh Mathematics which involve the study of right angles , its sides and trigonometric ratios.
the equation given in the question is
Sin (3y - 30°) = Cos (7y +50°)
cos(90 - ) = sin
Therefore
sin(3y-30°) = sin( 90-(7y+50°)
Equating the terms
3y - 30 = 90-7y -50
4y = 90-50+30
4y = 120-50
4y = 70
y = 17.5
The value for y is 17.5°
To know more about Trigonometry
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Answer:
12 foot.
Step-by-step explanation:
Given that,
A ladder leans a 15 foot ladder against a second story window.
The distance on the ground between the base of the ladder and the house is 9 feet.
We need to find the height of the ladder. Let it is h.
If we consider a right angles triangle such that 15 foot is hypotenuse, 9 feet is base, then we need to find the perpendicular height of the triangle. Using Pythagoras theorem to find it.
So, the height of the ladder that reaches the second story window is 12 foot.