Using Unit Circle to Find Sine, Cosine, and Tangent
Read this topicExplanations 4
- The unit circle is a circle with radius 1 centered at the origin of the Cartesian Plane. In a pair of coordinates (x,y)(x,y)(x,y) on the unit circle x2+y2=1x^2+y^2=1x2+y2=1, coo…
By Qinzhuo Zhang, Victor Wang
- (Video) Find Cos and Sin Values Using the Unit Circle Hand Trick! by Paris Mielke In this video by Paris Mielke, you will learn the hand trick to use the unit circle!
By Paris, Anusha Rahman
- Consider the following diagram: Here, we can see that having picked the point (a,b)(a,b)(a,b) in the first quadrant of the plane, the line from the origin to (a,b)(a,b)(a,b) for…
By Ruiran Xun, Anusha Rahman
- Visualising Sine, Cosine, and Tangent in a Unit Circle Mathematicians came up with a way to neatly represent sin\sinsin, cos\coscos, and tan\tantan of an angle, by inscribing…
By Harshita Singh Chauhan, Alex Federspiel, Anusha Rahman
Problems 51
- Given that θ=60º\theta = 60ºθ=60º (or if you prefer, π3\frac{\pi}{3}3π radians), what are the x-y coordinates of the point PPP?
- Let xxx be a real number such that the five numbers cos(2πx)\cos(2 \pi x)cos(2πx), cos(4πx)\cos(4 \pi x)cos(4πx), cos(8πx)\cos(8 \pi x)cos(8πx), cos(16πx)\cos(16 \pi x)cos(1…
- For every positive integer nnn, define SnS_nSn to be the sum Sn=∑k=12010(cosk!π2010)n.S_n = \sum_{k = 1}^{2010} \left( \cos \frac{k! \pi}{2010} \right)^n .Sn=k=1∑2010(cos201…
- If zzz is a complex number such that z=cis(θ)z = \text{cis}(\theta)z=cis(θ) for some angle θ\thetaθ and z+z−1=3,z + z^{-1} = \sqrt{3},z+z−1=3, what is the value of z2010+z−2010…
- The point PPP is on the unit circle. If the yyy-coordinate of PPP is , and PPP is in quadrant II, find the xxx coordinate.
- The point PPP is on the unit circle. If the xxx-coordinate of PPP is , and PPP is in quadrant IV, find the yyy coordinate.
- If and θ\thetaθ is in the 4th4^{\text{th}}4th quadrant, find sin(θ)\sin(\theta)sin(θ).
- If and θ\thetaθ is in the 1st1^{\text{st}}1st quadrant, find sin(θ)\sin(\theta)sin(θ).
- If and θ\thetaθ is in the 2nd2^{\text{nd}}2nd quadrant, find cos(θ)\cos(\theta)cos(θ).
- If and θ\thetaθ is in the 3rd3^{\text{rd}}3rd quadrant, find cos(θ)\cos(\theta)cos(θ).
- Give exact values for (cosθ,sinθ)(\cos\theta,\sin\theta)(cosθ,sinθ) for .
- Give exact values for (cosθ,sinθ)(\cos\theta,\sin\theta)(cosθ,sinθ) for .
- Give exact values for (cosθ,sinθ)(\cos\theta,\sin\theta)(cosθ,sinθ) for .
- Give exact values for (cosθ,sinθ)(\cos\theta,\sin\theta)(cosθ,sinθ) for 5π5\pi5π.
- Give exact values for (cosθ,sinθ)(\cos\theta,\sin\theta)(cosθ,sinθ) for .
- Give exact values for (cosθ,sinθ)(\cos\theta,\sin\theta)(cosθ,sinθ) for .
- Give exact values for (cosθ,sinθ)(\cos\theta,\sin\theta)(cosθ,sinθ) for .
- Give exact values for (cosθ,sinθ)(\cos\theta,\sin\theta)(cosθ,sinθ) for 10π10\pi10π.
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same sine value as π3\frac{\pi}33π
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same sine value as 80∘80^{\circ}80∘
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same sine value as 140∘140^{\circ}140∘
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same sine value as 4π3\frac{4\pi}334π
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same sine value as 305∘305^{\circ}305∘
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same sine value as 15∘15^{\circ}15∘
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same sine value as 160∘160^{\circ}160∘
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same sine value as 340∘340^{\circ}340∘
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same sine value as π4\frac{\pi}44π
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same sine value as 7π6\frac{7\pi}667π
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same cosine value as 80∘80^{\circ}80∘
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same cosine value as 140∘140^{\circ}140∘
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same cosine value as 305∘305^{\circ}305∘
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same cosine value as 15∘15^{\circ}15∘
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same cosine value as 160∘160^{\circ}160∘
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same cosine value as 340∘340^{\circ}340∘
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same cosine value as π3\frac{\pi}33π
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same cosine value as 4π3\frac{4\pi}334π
- Compute cosπ4\cos \frac{\pi}4cos4π.
- Find an angle θ\thetaθ with 0<θ<360∘0<\theta<360^{\circ}0<θ<360∘ or 0<θ<2π0<\theta<2\pi0<θ<2π that has the same cosine value as 7π6\frac{7\pi}667π
- If , and θ\thetaθ is in quadrant II, find cos(θ)\cos(\theta)cos(θ).
- If , and θ\thetaθ is in quadrant II, find cos(θ)\cos(\theta)cos(θ).
- If , and θ\thetaθ is in quadrant III, find sin(θ)\sin(\theta)sin(θ).
- If , and θ\thetaθ is in quadrant I, find sin(θ)\sin(\theta)sin(θ).
- If , and , find sin(θ)\sin(\theta)sin(θ).
- If , and , find cos(θ)\cos(\theta)cos(θ).
- If tan(θ)=4\tan(\theta)=4tan(θ)=4, and , find sin(θ)\sin(\theta)sin(θ).
- If tan(θ)=4\tan(\theta)=4tan(θ)=4, and , find cos(θ)\cos(\theta)cos(θ).
- Find sin(A)\sin(A)sin(A).
- Find cos(A)\cos(A)cos(A).
- Find sin(A)\sin(A)sin(A).
- Find cos(A)\cos(A)cos(A).
- On October 12, 1492, after departing from the Canary Islands, Christopher Columbus sighted land which he mistook for an island off the coast of China, but in reality was what we…