what would tan be for -1^(9)to the nearest degree? and what would sin -1^(0.62) be to the nearest degree?
.........srry idk
why post such questions that can be simply evaluated on any decent calculator? Or by google?
If you mean tan^-1(9) then that is 83.65°
sin^-1(0.62) = 38.32°
To calculate the values of trigonometric functions such as tangent (tan) and sine (sin) for given numbers, we can follow these steps:
1. Understanding the notation: The expression -1^(9) means raising -1 to the power of 9. However, -1 raised to any odd power will always be -1, and -1 raised to any even power will be 1. Therefore, -1^(9) equals -1.
2. Calculating the tangent (tan) value for -1: The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. Since the value -1 is not an angle, we cannot directly calculate its tangent. It's important to note that tangent is periodic and repeats every 180 degrees, so we can find an equivalent angle within a 180° interval.
To find the nearest degree, let's find an equivalent angle between 0 and 180 degrees that has the same tangent as -1. We can use algebraic reasoning to find this angle. Let's assume the angle is x degrees:
tan(x) = -1
Divide both sides of the equation by cos(x) to isolate tan(x):
tan(x) / cos(x) = -1 / cos(x)
tan(x) = -sin(x) / cos(x)
Now, substitute -1 for tan(x) in the equation:
-1 = -sin(x) / cos(x)
Since -sin(x) / cos(x) is the negative of the tangent of x degrees, we can say:
-1 = tan(-x)
This implies that -x is the equivalent angle to -1.
Therefore, the answer to the nearest degree is -x = -1.
Hence, tan(-1) to the nearest degree is -1.
3. Calculating the sine (sin) value for -1^(0.62): Similar to the previous step, the expression -1^(0.62) means raising -1 to the power of 0.62. However, when raising a negative number to a non-integer power, the result is usually a complex number. Therefore, finding the sine of this value is not possible using conventional trigonometric functions.
If you intended to calculate the sine of an angle, please provide the correct input in degrees or radians so that I can help you solve it accurately.