tan 0=1
csc 0 = sqrt. 2
cos 0 = sin 0
os 0 = cos (-pie/6)
The 0s means that symbol for angle. Please someone help me do these problems.
What is the interval of theta for which they want the answers? 0 to 2 pi?
tan theta = 1 at theta = pi/4 (45 degrees) and (in the third quadrant) at 5 pi/4
csc theta = sqrt 2 where sin theta = 1/sqrt2 which is also at pi/4, with a second-quadrant solution at 3 pi/4
cos theta = sin theta where tan theta = 1. Refer to the first answer
If your last question is
cos theta = cos -pi/6,
one obvious solution is
theta = -pi/6,
which would be the same as 11 pi/6 in the 0 to 2pi range. The other answer would be just pi/6 in the first quadrant, where the cosine has the same positivee sign as the fourth quadrant.
thanks, yes sorry the interval was 0 to 2pie
Sure! I can help you solve these trigonometric problems.
1. tan 0 = 1:
To find the value of 0 for which tan 0 equals 1, you can use the inverse tangent function (also known as arctan) on your calculator. The inverse tangent function will give you the angle that has a tangent value of 1. So, you would find the inverse tangent of 1, which gives the angle 45 degrees or π/4 radians.
2. csc 0 = √2:
To find the value of 0 for which csc 0 equals √2, you can use the inverse cosecant function (also known as arccsc) on a calculator. The inverse cosecant function gives you the angle whose cosecant value is √2. The inverse cosecant of √2 is approximately 70.53 degrees or 5π/6 radians.
3. cos 0 = sin 0:
To find the value of 0 for which cos 0 equals sin 0, you can use the inverse cosine function (also known as arccos) on a calculator. The inverse cosine function will give you the angle whose cosine value is equal to its sine value. By solving for this angle, you will find that 0 is equal to 45 degrees or π/4 radians.
4. sec 0 = cos(-π/6):
To find the value of 0 for which sec 0 equals cos(-π/6), you can use the inverse secant function (also known as arcsec) on a calculator. The inverse secant function gives you the angle whose secant value is equal to the given value. In this case, you would find the inverse secant of cos(-π/6), which gives you the angle π/6 or approximately 30 degrees.
Remember to use the appropriate function (arctan, arccsc, arccos, arcsec) on your calculator to find the inverse of the trigonometric functions.