Use the unit circle to verify that the cosine andsecant functions are even and t

Question

Use the unit circle to verify that the cosine andsecant functions are even and that the sine, cosecant, tangent, andcotangent functions are odd. - I know that th even functions are even because they aresymmetric with the y-axis, and that the odd functions are symmetricwith the origin, I get that. I don't understand how I can verifysec=1/x. I'm just confused. Please help! Use the unit circle to verify that the cosine andsecant functions are even and that the sine, cosecant, tangent, andcotangent functions are odd. - I know that th even functions are even because they aresymmetric with the y-axis, and that the odd functions are symmetricwith the origin, I get that. I don't understand how I can verifysec=1/x. I'm just confused. Please help!

Explanation / Answer

sometimes it's hard to tell if a function is symmetrical ornot. Another way to tell if a function is even or odd is that if f(-x) = f(x), then f(x) is even. If f(-x) = - f(x), thenf(x) is odd. For example in the unit circle, sin() = y.(y >=0) then - should be in the fourth quadrant. so sin(-) = -y [since in the fourth quadrant, they is negative] = -sin() (y >=0) so sin() is an odd function. sec() = 1/x (x >=0) since - is in the fourth quadrant, x is stillpositive so sec(-) = 1/x = sec() (x >=0) so sec() is an even function. etc.

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.