Respuesta :
Answer:
True; quadrants I & IV
Step-by-step explanation:
We know the relation between sine and cosine function which is given by
[tex]\sin^2 \theta +\cos^2 \theta = 1[/tex]
Let us solve this equation for cosine function.
[tex]\cos^2 \theta = 1-\sin^2 \theta [/tex]
Take square root both sides. When ever we take square root we need to write the solution in plus minus form
[tex]\sqrt{\cos^2 \theta}=\pm\sqrt{1-\sin^2 \theta} [/tex]
[tex]\cos \theta=\pm\sqrt{1-\sin^2 \theta} [/tex]
[tex]\cos \theta=-\sqrt{1-\sin^2 \theta}, \sqrt{1-\sin^2 \theta} [/tex]
If Θ is in quadrants I and IV then the value will be positive and if Θ is in II and III quadrant then the value is negative.
Hence, if Θ is in quadrants I & IV, then we have
[tex]\cos \theta=\sqrt{1-\sin^2 \theta} [/tex]
Thus, the correct option is: True; quadrants I & IV
The value Θ is in quadrants I and IV then the value will be positive then the correct option is True; quadrants I & IV.
What is a quadrant?
A quadrant is a region defined by the two axes (x-axis and y-axis) of the coordinate system.
- The sin and cosine of any angle, α is positive in the first quadrant 0-90,
- Sine is positive in 90-180, and the cosine in the fourth quadrant 270-360.
The equation which shows the relation between sin and cos angle is;
[tex]\rm Sin^2\theta+ Cos^2\theta=1\\\\Cos^2\theta=1- Sin^2\theta\\\\Cos\theta=\pm\sqrt{1-Sin^2\theta}[/tex]
Hence, If Θ is in quadrants I and IV then the value will be positive then the correct option is True; quadrants I & IV.
To know more about Quadrant click the link given below.
https://brainly.com/question/25876683
