Transformations of Trigonometric Functions

Amplitude
Sketch the graphs of each trigonometric function on the same coordinate system. How does the value of a affect the graphs of sine and cosine?[br]A) [img]data:image/png;base64,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[/img][br]B) [img]data:image/png;base64,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[/img][br]C) [img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFQAAAAhCAYAAABHhIyzAAAAAXNSR0IArs4c6QAAA/hJREFUaEPtmVnoTVEUxn9/L3gzDxmSeDBkiiQZC5llLBJeUIbMSTKUTFHGUGSKMiehDBmSZE4hQyJjUR4kSuJ8rKNzj3Nv93/vPv97b531coez19prf/tb31773jISc4pAmdNouQfrCVzO3b14PAsN6CbgB9AB6FU8sOSeSaEBVeZi59IE0Nw3MeyZAOoOyz+REkATQNMjkGioY3YkgCaAOkbAcbhCM3QF0AwY461rma1tueM1ZhvuADAuy8Fq8yLzLDSgWeYf+7BpwAfgWJYzCcxLUbe7BFBoDcwDJmYJpj9MV2W1fCmWAAqzgVvAtXICugU4DZwN+oUBPQV8AiYFBqXVi3Im4GL4YGA8cBtYGwg4Fdhmn296i+wcePbL3t8AukQkcQiYA7wNPJOezwdOAmOB1UBtYIi9aqjeTwBGpANU9K0GDPUAfWWHhBawEOgakYifaCag2gIPXCBp5dXDDoMXlqN+UNGGV7LXhsBroAbw2QC87vmIODuA94HDz09LQDYI5Sh9VGxhMtfTV23YG/7Kw0MbW8s0VN/9s6iSfwT0NpFWspWBRY5A8cO0AJpkiJlSRkAfYB2gDZK1tFeBpnJtD3y07wSG2CUWi2kjgRmAmPs1NGdTL+aJQNxwSvLXHBvT5CpSpWAYBrSV0VytjOwesMBj6PkYAG2UIea50LPNBoaqJWgCanjgl6qaJlmNjakauxMYBjyJqDT9bLjLNiQqHcmE2HnfWiq1VkH77slBleAXYUAXA22A0cbML0BV4GfEbNmUvLRMzMjX9tnCrwQCieErPY17akzUI2m/2CzdG2Vjj5imCpzweqWL8q+eBQP3hDqBel6lHAa6ZwJ0su3mAHNWYn3zRcOBf38r8/UGlBYi1mmzVf5LgI4eCVZ5DJ1ubNwN6CS+E/CJkjhpaCfgneXpa63kTiYftUgvQ4AKG23E1kyA6tkzoDmw3XTUv8E4wCUyhFii3X4OfMswieSnnWnaBasiDVdnMsirrONWlipDWV1AUuEzNV2LKOCku1fNrx+w305z+fiVGPaX/Fw0Df+XdnjQQSsXDbhrf03EBaTiikHaeR0Waq6liWfinDAitpg9MN1VMkMuylOVnGJBQNUiaKf0ndoLUVqf47JuxqKjNoEOjzrW38U1Z7q46grUpKvDycYkjdLe//5YjCoDlZVOtbhNUlLf27wpNlFwQ+OeOyp+eS4wJfHjiG46+gd0ZiHQdDVnsdzlVRU6dKRJ0tTHrhZY0XGKBVCdpDo111Q0AK7nKwZA1XCr3PeapupALFkrNKAqc52Yuo/LNgCzShbNiKtYRa5FJ2XUpaHQm5wXBiWdfF4rj8k5AdQxsAmgjgH9DbG1syKFwFrSAAAAAElFTkSuQmCC[/img]
Period
Sketch the graphs of each trigonometric function on the same coordinate system. How does the value of b affect the graphs of sine and cosine?[br]A) [img]data:image/png;base64,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[/img][br]B) [img]data:image/png;base64,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[/img]
Shifts
Sketch the graphs of [math]y=cos\left(x+\frac{\pi}{2}\right)+2[/math] and [math]y=sin\left(x+\pi\right)-1[/math] on the same coordinate system. How do the values of h and k affect the graphs of sine and cosine?
Putting It All Together
Sketch one cycle of each of the following trig functions.[br]A) [math]y=3sin\left(4x\right)+1[/math][br]B) [math]y=-2cos\left(\frac{x}{3}\right)-2[/math][br]C) [math]y=\frac{1}{2}cos\left(x+\frac{\pi}{2}\right)+1[/math]
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Information: Transformations of Trigonometric Functions