find delta in each of the following case:
tan delta=-0.75
The domain of tan(x) is from -π/2 to π/2. So the reference angle for tan(δ)=-0.75 is between -&pi/2; to 0.
Having found the reference angle δ (approx. -0.64 radians), the general solution will be
δ+kπ where k=an integer.
so what will be the solution
A pre-calculus answer is -0.64 + kπ radians, where k∈ℤ.
The reason for the kπ is because tangent is a periodic function, with period equal to π radians.
Also, for your solution, you will need to evaluate more accurately (accuracy according to instructions, 3-4 decimals normally) the value of arctan(-0.75).
To find the value of delta in the equation tan(delta) = -0.75, we can use inverse trigonometric functions. The inverse of the tangent function is arctan or atan.
Here's how you can find the value of delta:
1. Take the inverse tangent (arctan) of both sides of the equation:
arctan(tan(delta)) = arctan(-0.75)
2. Since arctan and tan are inverse functions, they cancel each other out, leaving us with:
delta = arctan(-0.75)
3. Use a calculator or a trigonometric table to find the arctan(-0.75) value.
By inputting -0.75 into the arctan function, you will get the result in radians or degrees depending on the calculator or settings used. Ensure that your calculator is set to the desired unit (radians or degrees) before finding the inverse tangent.
For example, if you're using a scientific calculator:
- Press the inverse tangent (arctan or atan) button.
- Input -0.75.
- Press the equals (=) button.
The result will give you the value of delta, expressed in either radians or degrees, depending on the calculator settings.