Tan theta=1
Can theta=-3pi/4?
How?
Tanθ=sinθ/cosθ
sin(-3π/4)=-(1/2)√2
cos(-3π/4)=-(1/2)√2
=>
Tan(-3π/4)=sin(-3π/4)/cos(-3π/4)
=[-(1/2)√2]/[-(1/2)√2]
=1
Thanks but i dont want tan theta= 1 to prove i want the value of theta is -3pi/4
Kindly elaborate your question:
Do you want to find tan(-3π/4), or do you want to prove tan(-3π/4)=1, or solve tan(x)=1 ???
yes
-3π/4 radians = -135°
-135° is in quadrant III by the CAST rule.
-135° is in the same position as 225° or (180° + 45°) .
the equivalent angle in standard position is 45°
so tan (-135°) = tan (-3π/4) = 1
Thanku reiny
To determine if theta can equal -3pi/4 when tan(theta) = 1, we can start by finding the reference angle associated with -3pi/4.
The reference angle is the positive acute angle between the terminal side of an angle in standard position and the x-axis. To find the reference angle, we can obtain the equivalent angle within one full revolution (360 degrees) or 2pi radians.
In this case, -3pi/4 is a negative angle measured clockwise starting from the positive x-axis. To find the equivalent positive angle, we can add one full revolution (2pi radians) to -3pi/4:
-3pi/4 + 2pi = 5pi/4
Therefore, the equivalent angle in one full revolution is 5pi/4.
Now, we can verify if tan(theta) = 1 when theta = 5pi/4:
tan(5pi/4) = sin(5pi/4) / cos(5pi/4)
Using the unit circle, we know that sin(5pi/4) = -sqrt(2)/2 and cos(5pi/4) = -sqrt(2)/2.
Plugging these values into the tangent equation:
tan(5pi/4) = (-sqrt(2)/2) / (-sqrt(2)/2) = 1
Since tan(theta) = 1 is true when theta = 5pi/4, we cannot conclude that theta = -3pi/4.
Therefore, theta cannot equal -3pi/4 when tan(theta) = 1.