Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
θ=2π+kπ,k∈Z
Alternative Form
θ=90∘+180∘k,k∈Z
Alternative Form
θ≈1.570796+kπ,k∈Z
Evaluate
sin2(θ)−1=0
Move the constant to the right-hand side and change its sign
sin2(θ)=0+1
Removing 0 doesn't change the value,so remove it from the expression
sin2(θ)=1
Take the root of both sides of the equation and remember to use both positive and negative roots
sin(θ)=±1
Simplify the expression
sin(θ)=±1
Separate the equation into 2 possible cases
sin(θ)=1sin(θ)=−1
Calculate
More Steps
Evaluate
sin(θ)=1
Use the inverse trigonometric function
θ=arcsin(1)
Calculate
θ=2π
Add the period of 2kπ,k∈Z to find all solutions
θ=2π+2kπ,k∈Z
θ=2π+2kπ,k∈Zsin(θ)=−1
Calculate
More Steps
Evaluate
sin(θ)=−1
Use the inverse trigonometric function
θ=arcsin(−1)
Calculate
θ=23π
Add the period of 2kπ,k∈Z to find all solutions
θ=23π+2kπ,k∈Z
θ=2π+2kπ,k∈Zθ=23π+2kπ,k∈Z
Solution
θ=2π+kπ,k∈Z
Alternative Form
θ=90∘+180∘k,k∈Z
Alternative Form
θ≈1.570796+kπ,k∈Z
Show Solution
Rewrite the equation
x2=0
Evaluate
sin2(θ)−1=0
Multiply both sides
(rsin(θ))2−r2=0
Use substitution
More Steps
Evaluate
(rsin(θ))2−r2
To covert the equation to rectangular coordinates using conversion formulas,substitute rsinθ for y
y2−r2
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
y2−(x2+y2)
Simplify the expression
−x2
−x2=0
Solution
x2=0
Show Solution
Graph
