Simplify & proving(Trigs)
Simplify sin^2(x)+cos^2(x)
Hint: This is the couple that’s always together. No matter what happens, they equal=? because they’re that solid.
1
solve sin(x)=0, 0∘≤x<360∘
Hint: It’s like when you show up to a party and no one’s there—sine just can’t find its “happy place.”
0∘,180∘
f(x)=1/x−3
Hint: Think of it as the “no-go zone” in a breakup. You just can’t go there. It’s an emotional black hole!
x=3
3x^2+5/2x^2-7
Hint: Horizontal asymptotes are like long-distance relationships—what happens when you’re really far away matters more than the messy details up close.
y=3/2
Simplify sin(x)/cos(x)+cos(x)sin(x)
Hint: This is like when two exes compete to outshine each other, only to end up combining into something unnecessarily complicated.
csc(x)sec(x)
They’re both extra, but now they’re a power couple.
Solve for (x); cos(x)=1/2, 0∘≤x<360∘
x=60∘,300∘
f(x)=x+2/x-1
Hint: "Why don’t denominators get invited to parties?
Because they always bring division!"
x=1
5x+3/2x^2+7
Hint: It’s like that one overachiever friend whose influence shrinks the more people they’re around. Eventually, they don’t even matter.
y=0(degree of the numerator is less than the denominator)
Prove 1+tan2(x)=sec2(x)
Hint: This is like when tangent thinks they’re independent, but secant steps in like, “You literally can’t exist without me.” Classic clingy friend vibes.
Use the Pythagorean identity
tangent is just secant’s sidekick, even if it doesn’t admit it.
Solve for x, sin(x)=√3/2, 0∘≤x<360∘
hint: It’s like your friend saying, “I’m not that predictable,” but always showing up at the same two places when you ask them to hang out
x=60∘,120∘
X^2+5x+6/x+3
Hint: This is like a friendship group where two people secretly cancel each other out. Who’s still hanging around?
x=3
F(x)=5x^3+7/3x^3-2x
When the strongest competitors (highest degree terms) face off, everyone else’s contributions are just background noise.
y=5/3
Simplify sin^2(x)/1-cos(x)
Hint: This problem wants to test your patience, just like when someone keeps typing..."in texts.
1+cos(x)
Solve for x: 2sin(x)−1=0, 0∘≤x<360∘
Hint; It’s like that moment when you find out your crush likes the same exact thing you do. Too easy? Maybe. Still exciting? Definitely
x=30∘,150∘
f(x)=2/x^2-4
Hint: It’s like trying to avoid drama between two exes at a party. Where are the spots you absolutely can’t go?
x=2 x=-2
f(x)=10x^2+7x+1/3x+4
Hint:This is like when someone brings up a wild story from 10 years ago—it doesn’t matter now because they’ve outgrown that phase. (The numerator wins here.)
0 because, the degree of the numerator is greater than the degree of the denominator,
cot^2(x)+1=csc^2(x)
Hint: Cotangent and cosecant are like the introverts of trig—they need each other to survive
Use the reciprocal identity
Solve for x: cos(2x)=1/2, 0∘≤x<360∘
Hint: When you and your BFF both get invited to the same party... 4 times. But hey, you don’t mind—more snacks, right?
x=30∘,150∘,210∘,300∘
f(x)=1/(x+1)(x-3)
Hint: This is like dealing with two super dramatic friends. The second you hit either of their triggers, chaos erupts!
x=-1 x=3
F(x)=X^3+5x/2x^3+9x^2+3
Hint: Imagine two people in a relationship competing to "win the breakup." The one with the highest power always dominates in the long run!
y=1/2