Question

*see attached image*

Hi, my tutor sent this to me and I'm confused about what -1 represents. If anyone can give me a detailed solution to this question it would be greatly appreciated

Answer 1

Sin, Cos, Tan and others are used to calculate the ratios of the sides of a right angled triangle by taking a certain angle as the angle of reference.

On the other hand, Sin‐¹, Cos‐¹ and Tan-¹ are used to find the reference angle used to calculate the ratio of sides.

For this question,

we need to find which option should used to calculate the angle the slide makes with the vertical support.

So the option will have to be either A, C or E.

here, the base is 2.81m and hypotenuse is 3.64m.

we know, Cos = base / hypotenuse

So the angle is given by Cos-¹(2.81/3.64)

Option C

Answer 2

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Answer:

E. sin⁻¹(2.81/3.64)

Explanation:

If you understand the question, you know that the relation of interest is ...

Sin = Opposite/Hypotenuse

sin(•) = 2.81/3.64

• = arcsin(2.81/3.64) . . . . matches choice E

If you want to find the angle, you need to use a function that gives the angle for a particular sine value. That function is called the arcsine function, or the inverse sine function. It is represented using the notation arcsin( ) or sin⁻¹( ). (The -1 is interpreted as being an exponent.)

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You may recall the rules of exponents say ...

s^-2 = 1/s^2

Then the simple reciprocal, or inverse, is ...

s^-1 = 1/s^1 = 1/s

That is, an exponent of -1 signifies an inverse. This is the notation of choice to signify an inverse function. It is applied to the function name. (It does not mean the reciprocal of the function value.)

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Additional comment

One needs to be careful with exponents on function names. An exponent of -1 on the name is generally understood to signify the inverse function.

Positive exponents greater than 1 can be ambiguous. Usually, we intend ...

`\sin^2(x) = (\sin(x))^2`

Sometimes, we mean ...

`f(f(x)) = f^2(x) \\e (f(x))^2 = f(x)^2`